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Theorem bnj118 29241
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj118.1
bnj118.2
Assertion
Ref Expression
bnj118
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,)   (,)   (,)   (,,)

Proof of Theorem bnj118
StepHypRef Expression
1 bnj118.2 . 2
2 bnj118.1 . . 3
3 bnj105 29090 . . 3
42, 3bnj91 29233 . 2
51, 4bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wceq 1653  wsbc 3162  c0 3629  cfv 5455  c1o 6718   c-bnj14 29053 This theorem is referenced by:  bnj151  29249  bnj153  29252 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-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pow 4378 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  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-v 2959  df-sbc 3163  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-pw 3802  df-sn 3821  df-suc 4588  df-1o 6725
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