mmtheorems133 - Metamath Proof Explorer

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Statement List for Metamath Proof Explorer - 13201-13300 - Page 133 of 195

Type	Label	Description
Statement
Theorem	bnj384 13201	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ (ch /\ ph /\ th)))
Theorem	bnj385 13202	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ ch) /\ ph /\ th))
Theorem	bnj386 13203	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ (ch /\ ph) /\ th))
Theorem	bnj387 13204	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ ch /\ (ph /\ th)))
Theorem	bnj388 13205	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ ch) /\ (ph /\ th)))
Theorem	bnj389 13206	/\-manipulation. (The proof was shortened by Andrew Salmon, 14-Jun-2011.)
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ th /\ ph /\ ch))
Theorem	bnj390 13207	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ th /\ ph) /\ ch))
Theorem	bnj391 13208	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (((ps /\ th) /\ ph) /\ ch))
Theorem	bnj392 13209	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ (th /\ ph)) /\ ch))
Theorem	bnj393 13210	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ ((th /\ ph) /\ ch)))
Theorem	bnj394 13211	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ (th /\ (ph /\ ch))))
Theorem	bnj395 13212	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ (th /\ ph /\ ch)))
Theorem	bnj396 13213	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ th) /\ ph /\ ch))
Theorem	bnj397 13214	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ (th /\ ph) /\ ch))
Theorem	bnj398 13215	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ th /\ (ph /\ ch)))
Theorem	bnj399 13216	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ th) /\ (ph /\ ch)))
Theorem	bnj400 13217	/\-manipulation. (The proof was shortened by Andrew Salmon, 14-Jun-2011.)
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ ps /\ ph /\ th))
Theorem	bnj401 13218	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ch /\ ps /\ ph) /\ th))
Theorem	bnj402 13219	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (((ch /\ ps) /\ ph) /\ th))
Theorem	bnj403 13220	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ch /\ (ps /\ ph)) /\ th))
Theorem	bnj404 13221	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ ((ps /\ ph) /\ th)))
Theorem	bnj405 13222	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ (ps /\ (ph /\ th))))
Theorem	bnj406 13223	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ (ps /\ ph /\ th)))
Theorem	bnj407 13224	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ch /\ ps) /\ ph /\ th))
Theorem	bnj408 13225	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ (ps /\ ph) /\ th))
Theorem	bnj409 13226	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ ps /\ (ph /\ th)))
Theorem	bnj410 13227	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ch /\ ps) /\ (ph /\ th)))
Theorem	bnj411 13228	/\-manipulation. (The proof was shortened by Andrew Salmon, 14-Jun-2011.)
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ ps /\ ph /\ ch))
Theorem	bnj412 13229	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((th /\ ps /\ ph) /\ ch))
Theorem	bnj413 13230	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (((th /\ ps) /\ ph) /\ ch))
Theorem	bnj414 13231	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((th /\ (ps /\ ph)) /\ ch))
Theorem	bnj415 13232	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ ((ps /\ ph) /\ ch)))
Theorem	bnj416 13233	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ (ps /\ (ph /\ ch))))
Theorem	bnj417 13234	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ (ps /\ ph /\ ch)))
Theorem	bnj418 13235	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((th /\ ps) /\ ph /\ ch))
Theorem	bnj419 13236	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ (ps /\ ph) /\ ch))
Theorem	bnj420 13237	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ ps /\ (ph /\ ch)))
Theorem	bnj421 13238	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((th /\ ps) /\ (ph /\ ch)))
Theorem	bnj422 13239	/\-manipulation. (The proof was shortened by Andrew Salmon, 14-Jun-2011.)
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ th /\ ph /\ ps))
Theorem	bnj423 13240	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ch /\ th /\ ph) /\ ps))
Theorem	bnj424 13241	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (((ch /\ th) /\ ph) /\ ps))
Theorem	bnj425 13242	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ch /\ (th /\ ph)) /\ ps))
Theorem	bnj426 13243	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ ((th /\ ph) /\ ps)))
Theorem	bnj427 13244	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ (th /\ (ph /\ ps))))
Theorem	bnj428 13245	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ (th /\ ph /\ ps)))
Theorem	bnj429 13246	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ch /\ th) /\ ph /\ ps))
Theorem	bnj430 13247	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ (th /\ ph) /\ ps))
Theorem	bnj431 13248	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ th /\ (ph /\ ps)))
Theorem	bnj432 13249	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ch /\ th) /\ (ph /\ ps)))
Theorem	bnj434 13250	/\-manipulation. (The proof was shortened by Andrew Salmon, 14-Jun-2011.)
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ ch /\ ph /\ ps))
Theorem	bnj435 13251	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((th /\ ch /\ ph) /\ ps))
Theorem	bnj436 13252	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (((th /\ ch) /\ ph) /\ ps))
Theorem	bnj437 13253	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((th /\ (ch /\ ph)) /\ ps))
Theorem	bnj438 13254	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ ((ch /\ ph) /\ ps)))
Theorem	bnj439 13255	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ (ch /\ (ph /\ ps))))
Theorem	bnj440 13256	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ (ch /\ ph /\ ps)))
Theorem	bnj441 13257	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((th /\ ch) /\ ph /\ ps))
Theorem	bnj442 13258	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ (ch /\ ph) /\ ps))
Theorem	bnj443 13259	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ ch /\ (ph /\ ps)))
Theorem	bnj444 13260	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((th /\ ch) /\ (ph /\ ps)))
Theorem	bnj445 13261	/\-manipulation. (The proof was shortened by Andrew Salmon, 14-Jun-2011.)
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ ch /\ th /\ ph))
Theorem	bnj446 13262	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ ch /\ th) /\ ph))
Theorem	bnj447 13263	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (((ps /\ ch) /\ th) /\ ph))
Theorem	bnj448 13264	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ (ch /\ th)) /\ ph))
Theorem	bnj449 13265	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ ((ch /\ th) /\ ph)))
Theorem	bnj450 13266	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ (ch /\ (th /\ ph))))
Theorem	bnj451 13267	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ (ch /\ th /\ ph)))
Theorem	bnj452 13268	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ ch) /\ th /\ ph))
Theorem	bnj453 13269	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ (ch /\ th) /\ ph))
Theorem	bnj454 13270	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ ch /\ (th /\ ph)))
Theorem	bnj455 13271	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ ch) /\ (th /\ ph)))
Theorem	bnj456 13272	/\-manipulation. (The proof was shortened by Andrew Salmon, 14-Jun-2011.)
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ th /\ ch /\ ph))
Theorem	bnj457 13273	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ th /\ ch) /\ ph))
Theorem	bnj458 13274	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (((ps /\ th) /\ ch) /\ ph))
Theorem	bnj459 13275	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ (th /\ ch)) /\ ph))
Theorem	bnj460 13276	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ ((th /\ ch) /\ ph)))
Theorem	bnj461 13277	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ (th /\ (ch /\ ph))))
Theorem	bnj462 13278	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ (th /\ ch /\ ph)))
Theorem	bnj463 13279	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ th) /\ ch /\ ph))
Theorem	bnj464 13280	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ (th /\ ch) /\ ph))
Theorem	bnj465 13281	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ps /\ th /\ (ch /\ ph)))
Theorem	bnj466 13282	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ps /\ th) /\ (ch /\ ph)))
Theorem	bnj467 13283	/\-manipulation. (The proof was shortened by Andrew Salmon, 14-Jun-2011.)
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ ps /\ th /\ ph))
Theorem	bnj468 13284	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ch /\ ps /\ th) /\ ph))
Theorem	bnj469 13285	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (((ch /\ ps) /\ th) /\ ph))
Theorem	bnj470 13286	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ch /\ (ps /\ th)) /\ ph))
Theorem	bnj471 13287	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ ((ps /\ th) /\ ph)))
Theorem	bnj472 13288	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ (ps /\ (th /\ ph))))
Theorem	bnj473 13289	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ (ps /\ th /\ ph)))
Theorem	bnj474 13290	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ch /\ ps) /\ th /\ ph))
Theorem	bnj475 13291	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ (ps /\ th) /\ ph))
Theorem	bnj476 13292	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (ch /\ ps /\ (th /\ ph)))
Theorem	bnj478 13293	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((ch /\ ps) /\ (th /\ ph)))
Theorem	bnj479 13294	/\-manipulation. (The proof was shortened by Andrew Salmon, 14-Jun-2011.)
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ ps /\ ch /\ ph))
Theorem	bnj480 13295	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((th /\ ps /\ ch) /\ ph))
Theorem	bnj481 13296	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (((th /\ ps) /\ ch) /\ ph))
Theorem	bnj482 13297	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> ((th /\ (ps /\ ch)) /\ ph))
Theorem	bnj483 13298	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ ((ps /\ ch) /\ ph)))
Theorem	bnj484 13299	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ (ps /\ (ch /\ ph))))
Theorem	bnj485 13300	/\-manipulation.
|- ((ph /\ ps /\ ch /\ th) <-> (th /\ (ps /\ ch /\ ph)))