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Theorem bnj1175 29375
 Description: Technical lemma for bnj69 29381. 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
bnj1175.3
bnj1175.4
bnj1175.5
Assertion
Ref Expression
bnj1175

Proof of Theorem bnj1175
StepHypRef Expression
1 bnj1175.4 . . . . 5
2 bnj255 29071 . . . . 5
3 df-bnj17 29053 . . . . 5
41, 2, 33bitr2i 266 . . . 4
5 bnj1175.5 . . . . 5
65anbi1i 678 . . . 4
74, 6bitr4i 245 . . 3
8 bnj1125 29363 . . . . 5
91, 8bnj835 29130 . . . 4
10 bnj906 29303 . . . . . 6
111, 10bnj836 29131 . . . . 5
12 bnj1152 29369 . . . . . . 7
1312biimpri 199 . . . . . 6
141, 13bnj837 29132 . . . . 5
1511, 14sseldd 3351 . . . 4
169, 15sseldd 3351 . . 3
177, 16sylbir 206 . 2
1817ex 425 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937   wceq 1653   wcel 1726   cin 3321   wss 3322   class class class wbr 4214   w-bnj17 29052   c-bnj14 29054   w-bnj15 29058   c-bnj18 29060 This theorem is referenced by:  bnj1190  29379 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 4322  ax-sep 4332  ax-nul 4340  ax-pow 4379  ax-pr 4405  ax-un 4703  ax-reg 7562  ax-inf2 7598 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 4215  df-opab 4269  df-mpt 4270  df-tr 4305  df-eprel 4496  df-id 4500  df-po 4505  df-so 4506  df-fr 4543  df-we 4545  df-ord 4586  df-on 4587  df-lim 4588  df-suc 4589  df-om 4848  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-rn 4891  df-res 4892  df-ima 4893  df-iota 5420  df-fun 5458  df-fn 5459  df-f 5460  df-f1 5461  df-fo 5462  df-f1o 5463  df-fv 5464  df-1o 6726  df-bnj17 29053  df-bnj14 29055  df-bnj13 29057  df-bnj15 29059  df-bnj18 29061  df-bnj19 29063
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