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Theorem bnj154 29423
 Description: Technical lemma for bnj153 29425. 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
bnj154.1
bnj154.2
Assertion
Ref Expression
bnj154
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,)   (,)   (,,)   (,,)

Proof of Theorem bnj154
StepHypRef Expression
1 bnj154.1 . 2
2 bnj154.2 . . 3
32sbcbii 3228 . 2
4 vex 2968 . . 3
5 fveq1 5762 . . . 4
65eqeq1d 2451 . . 3
74, 6sbcie 3204 . 2
81, 3, 73bitri 264 1
 Colors of variables: wff set class Syntax hints:   wb 178   wceq 1654  wsbc 3170  c0 3616  cfv 5489   c-bnj14 29226 This theorem is referenced by:  bnj153  29425  bnj580  29458  bnj607  29461 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424 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 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-rex 2718  df-v 2967  df-sbc 3171  df-uni 4045  df-br 4244  df-iota 5453  df-fv 5497
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