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Theorem bnj1384 29475
 Description: Technical lemma for bnj60 29505. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1384.1
bnj1384.2
bnj1384.3
bnj1384.4
bnj1384.5
bnj1384.6
bnj1384.7
bnj1384.8
bnj1384.9
bnj1384.10
Assertion
Ref Expression
bnj1384
Distinct variable groups:   ,,,   ,   ,   ,,   ,,,   ,,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   ()   (,,)   (,,)   (,,,)   (,,,)   ()   (,)   (,,,)   (,,,)   (,,,)

Proof of Theorem bnj1384
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bnj1384.1 . . . . 5
2 bnj1384.2 . . . . 5
3 bnj1384.3 . . . . 5
4 bnj1384.4 . . . . 5
5 bnj1384.5 . . . . 5
6 bnj1384.6 . . . . 5
7 bnj1384.7 . . . . 5
8 bnj1384.8 . . . . 5
9 bnj1384.9 . . . . 5
10 bnj1384.10 . . . . 5
111, 2, 3, 4, 8bnj1373 29473 . . . . 5
121, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11bnj1371 29472 . . . 4
1312rgen 2773 . . 3
14 id 21 . . . . . 6
151, 2, 3, 4, 5, 6, 7, 8, 9bnj1374 29474 . . . . . 6
16 nfab1 2576 . . . . . . . . . 10
179, 16nfcxfr 2571 . . . . . . . . 9
1817nfcri 2568 . . . . . . . 8
19 nfab1 2576 . . . . . . . . . 10
203, 19nfcxfr 2571 . . . . . . . . 9
2120nfcri 2568 . . . . . . . 8
2218, 21nfim 1833 . . . . . . 7
23 eleq1 2498 . . . . . . . 8
24 eleq1 2498 . . . . . . . 8
2523, 24imbi12d 313 . . . . . . 7
2622, 25, 15chvar 1969 . . . . . 6
27 eqid 2438 . . . . . . 7
281, 2, 3, 27bnj1326 29469 . . . . . 6
2914, 15, 26, 28syl3an 1227 . . . . 5
30293expib 1157 . . . 4
3130ralrimivv 2799 . . 3
32 biid 229 . . . 4
33 biid 229 . . . 4
349bnj1317 29267 . . . 4
3532, 27, 33, 34bnj1386 29279 . . 3
3613, 31, 35sylancr 646 . 2
3710funeqi 5477 . 2
3836, 37sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360   w3a 937  wex 1551   wceq 1653   wcel 1726  cab 2424   wne 2601  wral 2707  wrex 2708  crab 2711  wsbc 3163   cun 3320   cin 3321   wss 3322  c0 3630  csn 3816  cop 3819  cuni 4017   class class class wbr 4215   cdm 4881   cres 4883   wfun 5451   wfn 5452  cfv 5457   c-bnj14 29126   w-bnj15 29130   c-bnj18 29132 This theorem is referenced by:  bnj1312  29501 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-rep 4323  ax-sep 4333  ax-nul 4341  ax-pow 4380  ax-pr 4406  ax-un 4704  ax-reg 7563  ax-inf2 7599 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-reu 2714  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-tp 3824  df-op 3825  df-uni 4018  df-iun 4097  df-br 4216  df-opab 4270  df-mpt 4271  df-tr 4306  df-eprel 4497  df-id 4501  df-po 4506  df-so 4507  df-fr 4544  df-we 4546  df-ord 4587  df-on 4588  df-lim 4589  df-suc 4590  df-om 4849  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894  df-iota 5421  df-fun 5459  df-fn 5460  df-f 5461  df-f1 5462  df-fo 5463  df-f1o 5464  df-fv 5465  df-1o 6727  df-bnj17 29125  df-bnj14 29127  df-bnj13 29129  df-bnj15 29131  df-bnj18 29133  df-bnj19 29135
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