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Theorem bnj1133 29360
 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
bnj1133.3
bnj1133.5
bnj1133.7
bnj1133.8
Assertion
Ref Expression
bnj1133
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   (,,)   (,,,)   (,,,)

Proof of Theorem bnj1133
StepHypRef Expression
1 bnj1133.5 . . 3
2 bnj1133.3 . . . 4
32bnj1071 29348 . . 3
41, 3bnj769 29133 . 2
5 impexp 435 . . . . . 6
65bicomi 195 . . . . 5
76albii 1576 . . . 4
8 bnj1133.8 . . . 4
97, 8mpgbir 1560 . . 3
10 df-ral 2712 . . 3
119, 10mpbir 202 . 2
12 vex 2961 . . 3
13 bnj1133.7 . . 3
1412, 13bnj110 29231 . 2
154, 11, 14sylancl 645 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550   wceq 1653   wcel 1726  wral 2707  wsbc 3163   cdif 3319  c0 3630  csn 3816   class class class wbr 4214   cep 4494   wfr 4540  com 4847   wfn 5451   w-bnj17 29052 This theorem is referenced by:  bnj1128  29361 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-sep 4332  ax-nul 4340  ax-pr 4405  ax-un 4703 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-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-sn 3822  df-pr 3823  df-tp 3824  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-tr 4305  df-eprel 4496  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-bnj17 29053
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