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Theorem bnj944 29310
 Description: Technical lemma for bnj69 29380. 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
bnj944.1
bnj944.2
bnj944.3
bnj944.4
bnj944.7
bnj944.10
bnj944.12
bnj944.13
bnj944.14
bnj944.15
Assertion
Ref Expression
bnj944
Distinct variable groups:   ,,,,   ,,,,   ,,,,   ,   ,,
Allowed substitution hints:   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   (,,,,,)   ()   (,,,,,)   (,,,,,)   ()   (,,,,,)   (,,,)   (,,,,,)   (,,,,,)

Proof of Theorem bnj944
StepHypRef Expression
1 simpl 445 . . . 4
2 bnj944.3 . . . . . . . 8
3 bnj667 29121 . . . . . . . 8
42, 3sylbi 189 . . . . . . 7
5 bnj944.14 . . . . . . 7
64, 5sylibr 205 . . . . . 6
763ad2ant1 979 . . . . 5
87adantl 454 . . . 4
92bnj1232 29176 . . . . . . 7
10 vex 2960 . . . . . . . 8
1110bnj216 29100 . . . . . . 7
12 id 21 . . . . . . 7
139, 11, 123anim123i 1140 . . . . . 6
14 bnj944.15 . . . . . . 7
15 3ancomb 946 . . . . . . 7
1614, 15bitri 242 . . . . . 6
1713, 16sylibr 205 . . . . 5
1817adantl 454 . . . 4
19 bnj253 29069 . . . 4
201, 8, 18, 19syl3anbrc 1139 . . 3
21 bnj944.12 . . . 4
22 bnj944.10 . . . . 5
23 bnj944.1 . . . . 5
24 bnj944.2 . . . . 5
2522, 5, 14, 23, 24bnj938 29309 . . . 4
2621, 25syl5eqel 2521 . . 3
2720, 26syl 16 . 2
28 bnj658 29120 . . . . . 6
292, 28sylbi 189 . . . . 5
30293ad2ant1 979 . . . 4
31 simp3 960 . . . 4
32 bnj291 29076 . . . 4
3330, 31, 32sylanbrc 647 . . 3
3433adantl 454 . 2
35 bnj944.7 . . . . 5
36 bnj944.13 . . . . . . 7
37 opeq2 3986 . . . . . . . . 9
3837sneqd 3828 . . . . . . . 8
3938uneq2d 3502 . . . . . . 7
4036, 39syl5eq 2481 . . . . . 6
41 dfsbcq 3164 . . . . . 6
4240, 41syl 16 . . . . 5
4335, 42syl5bb 250 . . . 4
4443imbi2d 309 . . 3
45 bnj944.4 . . . 4
46 biid 229 . . . 4
47 eqid 2437 . . . 4
48 0ex 4340 . . . . 5
4948elimel 3792 . . . 4
5023, 45, 46, 22, 47, 49bnj929 29308 . . 3
5144, 50dedth 3781 . 2
5227, 34, 51sylc 59 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937   wceq 1653   wcel 1726  wral 2706  cvv 2957  wsbc 3162   cdif 3318   cun 3319  c0 3629  cif 3740  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:  bnj910  29320 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-rep 4321  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-3or 938  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-reu 2713  df-rab 2715  df-v 2959  df-sbc 3163  df-csb 3253  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-pss 3337  df-nul 3630  df-if 3741  df-pw 3802  df-sn 3821  df-pr 3822  df-tp 3823  df-op 3824  df-uni 4017  df-iun 4096  df-br 4214  df-opab 4268  df-mpt 4269  df-tr 4304  df-eprel 4495  df-id 4499  df-po 4504  df-so 4505  df-fr 4542  df-we 4544  df-ord 4585  df-on 4586  df-lim 4587  df-suc 4588  df-om 4847  df-xp 4885  df-rel 4886  df-cnv 4887  df-co 4888  df-dm 4889  df-rn 4890  df-res 4891  df-ima 4892  df-iota 5419  df-fun 5457  df-fn 5458  df-f 5459  df-f1 5460  df-fo 5461  df-f1o 5462  df-fv 5463  df-bnj17 29052  df-bnj14 29054  df-bnj13 29056  df-bnj15 29058
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