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Theorem bnj1052 29345
 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
bnj1052.1
bnj1052.2
bnj1052.3
bnj1052.4
bnj1052.5
bnj1052.6
bnj1052.7
bnj1052.8
bnj1052.9
bnj1052.10
bnj1052.37
Assertion
Ref Expression
bnj1052
Distinct variable groups:   ,,,,   ,,,,   ,,,,   ,   ,,,,   ,   ,,,,   ,   ,   ,,,,   ,,,,   ,,   ,
Allowed substitution hints:   (,,,,)   (,,,,,)   (,,,,,)   (,)   (,)   (,,,,)   (,,,,,)   (,,,,,)   ()   (,)   (,,,,)   ()   (,,,,,)   ()

Proof of Theorem bnj1052
StepHypRef Expression
1 bnj1052.1 . 2
2 bnj1052.2 . 2
3 bnj1052.3 . 2
4 bnj1052.4 . 2
5 bnj1052.5 . 2
6 bnj1052.6 . 2
7 bnj1052.7 . 2
8 bnj1052.8 . 2
9 19.23vv 1916 . . . . 5
109albii 1576 . . . 4
11 19.23v 1915 . . . 4
1210, 11bitri 242 . . 3
13 bnj1052.37 . . . . 5
14 vex 2960 . . . . . . . . 9
15 bnj1052.10 . . . . . . . . 9
1614, 15bnj110 29230 . . . . . . . 8
17 bnj1052.9 . . . . . . . . 9
186, 17bnj1049 29344 . . . . . . . 8
1916, 18sylib 190 . . . . . . 7
201919.21bi 1775 . . . . . 6
2120, 17sylib 190 . . . . 5
2213, 21mpcom 35 . . . 4
2322gen2 1557 . . 3
2412, 23mpgbi 1559 . 2
251, 2, 3, 4, 5, 6, 7, 8, 24bnj1034 29340 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937  wal 1550  wex 1551   wceq 1653   wcel 1726  cab 2423  wral 2706  wrex 2707  cvv 2957  wsbc 3162   cdif 3318   wss 3321  c0 3629  csn 3815  ciun 4094   class class class wbr 4213   cep 4493   wfr 4539   csuc 4584  com 4846   wfn 5450  cfv 5455   w-bnj17 29051   c-bnj14 29053   w-bnj15 29057   c-bnj18 29059   w-bnj19 29061 This theorem is referenced by:  bnj1053  29346 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-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331 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-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-csb 3253  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-iun 4096  df-br 4214  df-fr 4542  df-fn 5458  df-bnj17 29052  df-bnj18 29060
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