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Theorem bnj557 29273
 Description: Technical lemma for bnj852 29293. 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
bnj557.3
bnj557.16
bnj557.17
bnj557.18
bnj557.19
bnj557.20
bnj557.21
bnj557.22
bnj557.23
bnj557.24
bnj557.25
bnj557.28
bnj557.29
bnj557.36
Assertion
Ref Expression
bnj557
Distinct variable groups:   ,,,   ,   ,,,   ,,,   ,,   ,
Allowed substitution hints:   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,)   (,,,,,,)

Proof of Theorem bnj557
StepHypRef Expression
1 df-bnj17 29052 . . . . . 6
2 bnj256 29071 . . . . . 6
31, 2bitr3i 244 . . . . 5
4 bnj557.18 . . . . . . . 8
5 bnj557.19 . . . . . . . 8
64, 5bnj556 29272 . . . . . . 7
763anim3i 1142 . . . . . 6
8 bnj557.20 . . . . . . 7
9 vex 2960 . . . . . . . 8
109bnj216 29100 . . . . . . 7
118, 10bnj837 29131 . . . . . 6
127, 11anim12i 551 . . . . 5
133, 12sylbir 206 . . . 4
145bnj1254 29182 . . . . . 6
158simp3bi 975 . . . . . 6
16 bnj551 29111 . . . . . 6
1714, 15, 16syl2an 465 . . . . 5
1817adantl 454 . . . 4
1913, 18jca 520 . . 3
20 df-3an 939 . . 3
2119, 2, 203imtr4i 259 . 2
22 bnj557.28 . . 3
23 bnj557.29 . . 3
24 bnj557.3 . . 3
25 bnj557.16 . . 3
26 bnj557.17 . . 3
27 bnj557.22 . . 3
28 bnj557.25 . . 3
29 bnj557.21 . . 3
30 bnj557.23 . . 3
31 bnj557.24 . . 3
32 bnj557.36 . . 3
3322, 23, 24, 25, 26, 4, 27, 28, 29, 30, 31, 32bnj553 29270 . 2
3421, 33syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937   wceq 1653   wcel 1726  wral 2706   cdif 3318   cun 3319  c0 3629  csn 3815  cop 3818  ciun 4094   csuc 4584  com 4846   wfn 5450  cfv 5455   w-bnj17 29051   c-bnj14 29053   w-bnj15 29057 This theorem is referenced by:  bnj558  29274 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 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404  ax-un 4702  ax-reg 7561 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-sbc 3163  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-iun 4096  df-br 4214  df-opab 4268  df-eprel 4495  df-id 4499  df-fr 4542  df-suc 4588  df-xp 4885  df-rel 4886  df-cnv 4887  df-co 4888  df-dm 4889  df-res 4891  df-iota 5419  df-fun 5457  df-fn 5458  df-fv 5463  df-bnj17 29052
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