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Theorem bnj985 29325
 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
bnj985.3
bnj985.6
bnj985.9
bnj985.11
bnj985.13
Assertion
Ref Expression
bnj985
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,)   (,,)   (,,)   (,,)   (,)   (,,)   (,,)

Proof of Theorem bnj985
StepHypRef Expression
1 bnj985.13 . . . 4
21bnj918 29136 . . 3
3 bnj985.3 . . . 4
4 bnj985.11 . . . 4
53, 4bnj984 29324 . . 3
62, 5ax-mp 8 . 2
7 sbcex2 3211 . . 3
8 nfv 1630 . . . . . . 7
98sb8e 2170 . . . . . 6
10 sbsbc 3166 . . . . . . 7
1110exbii 1593 . . . . . 6
129, 11bitri 242 . . . . 5
13 bnj985.6 . . . . 5
1412, 13bnj133 29093 . . . 4
1514sbcbii 3217 . . 3
16 bnj985.9 . . . 4
1716exbii 1593 . . 3
187, 15, 173bitr4i 270 . 2
196, 18bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   w3a 937  wex 1551   wceq 1653  wsb 1659   wcel 1726  cab 2423  wrex 2707  cvv 2957  wsbc 3162   cun 3319  csn 3815  cop 3818   wfn 5450   w-bnj17 29051 This theorem is referenced by:  bnj1018  29334 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 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-rex 2712  df-v 2959  df-sbc 3163  df-dif 3324  df-un 3326  df-nul 3630  df-sn 3821  df-pr 3822  df-uni 4017  df-bnj17 29052
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