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Theorem bnj944 31765
 Description: Technical lemma for bnj69 31835. 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 454 . . . 4
2 bnj944.3 . . . . . . . 8
3 bnj667 31578 . . . . . . . 8
42, 3sylbi 195 . . . . . . 7
5 bnj944.14 . . . . . . 7
64, 5sylibr 212 . . . . . 6
763ad2ant1 1004 . . . . 5
87adantl 463 . . . 4
92bnj1232 31631 . . . . . . 7
10 vex 2973 . . . . . . . 8
1110bnj216 31557 . . . . . . 7
12 id 22 . . . . . . 7
139, 11, 123anim123i 1168 . . . . . 6
14 bnj944.15 . . . . . . 7
15 3ancomb 969 . . . . . . 7
1614, 15bitri 249 . . . . . 6
1713, 16sylibr 212 . . . . 5
1817adantl 463 . . . 4
19 bnj253 31526 . . . 4
201, 8, 18, 19syl3anbrc 1167 . . 3
21 bnj944.12 . . . 4
22 bnj944.10 . . . . 5
23 bnj944.1 . . . . 5
24 bnj944.2 . . . . 5
2522, 5, 14, 23, 24bnj938 31764 . . . 4
2621, 25syl5eqel 2525 . . 3
2720, 26syl 16 . 2
28 bnj658 31577 . . . . . 6
292, 28sylbi 195 . . . . 5
30293ad2ant1 1004 . . . 4
31 simp3 985 . . . 4
32 bnj291 31533 . . . 4
3330, 31, 32sylanbrc 659 . . 3
35 bnj944.7 . . . . 5
36 bnj944.13 . . . . . . 7
37 opeq2 4057 . . . . . . . . 9
3837sneqd 3886 . . . . . . . 8
3938uneq2d 3507 . . . . . . 7
4036, 39syl5eq 2485 . . . . . 6
41 dfsbcq 3185 . . . . . 6
4240, 41syl 16 . . . . 5
4335, 42syl5bb 257 . . . 4
4443imbi2d 316 . . 3
45 bnj944.4 . . . 4
46 biid 236 . . . 4
47 eqid 2441 . . . 4
48 0ex 4419 . . . . 5
4948elimel 3849 . . . 4
5023, 45, 46, 22, 47, 49bnj929 31763 . . 3
5144, 50dedth 3838 . 2
5227, 34, 51sylc 60 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 960   wceq 1364   wcel 1761  wral 2713  cvv 2970  wsbc 3183   cdif 3322   cun 3323  c0 3634  cif 3788  csn 3874  cop 3880  ciun 4168   csuc 4717   wfn 5410  cfv 5415  com 6475   w-bnj17 31508   c-bnj14 31510   w-bnj15 31514 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1713  ax-7 1733  ax-8 1763  ax-9 1765  ax-10 1780  ax-11 1785  ax-12 1797  ax-13 1948  ax-ext 2422  ax-rep 4400  ax-sep 4410  ax-nul 4418  ax-pr 4528  ax-un 6371  ax-reg 7803 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 961  df-3an 962  df-tru 1367  df-ex 1592  df-nf 1595  df-sb 1706  df-eu 2261  df-mo 2262  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-ne 2606  df-ral 2718  df-rex 2719  df-reu 2720  df-rab 2722  df-v 2972  df-sbc 3184  df-csb 3286  df-dif 3328  df-un 3330  df-in 3332  df-ss 3339  df-pss 3341  df-nul 3635  df-if 3789  df-pw 3859  df-sn 3875  df-pr 3877  df-tp 3879  df-op 3881  df-uni 4089  df-iun 4170  df-br 4290  df-opab 4348  df-mpt 4349  df-tr 4383  df-eprel 4628  df-id 4632  df-po 4637  df-so 4638  df-fr 4675  df-we 4677  df-ord 4718  df-on 4719  df-lim 4720  df-suc 4721  df-xp 4842  df-rel 4843  df-cnv 4844  df-co 4845  df-dm 4846  df-rn 4847  df-res 4848  df-ima 4849  df-iota 5378  df-fun 5417  df-fn 5418  df-f 5419  df-f1 5420  df-fo 5421  df-f1o 5422  df-fv 5423  df-om 6476  df-bnj17 31509  df-bnj14 31511  df-bnj13 31513  df-bnj15 31515 This theorem is referenced by:  bnj910  31775
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