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Theorem bnj1534 29298
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1534.1
bnj1534.2
Assertion
Ref Expression
bnj1534
Distinct variable groups:   ,,,   ,,   ,,,
Allowed substitution hints:   (,,)   ()

Proof of Theorem bnj1534
StepHypRef Expression
1 bnj1534.1 . 2
2 nfcv 2574 . . 3
3 nfcv 2574 . . 3
4 nfv 1630 . . 3
5 bnj1534.2 . . . . . 6
65nfcii 2565 . . . . 5
7 nfcv 2574 . . . . 5
86, 7nffv 5738 . . . 4
9 nfcv 2574 . . . 4
108, 9nfne 2697 . . 3
11 fveq2 5731 . . . 4
12 fveq2 5731 . . . 4
1311, 12neeq12d 2618 . . 3
142, 3, 4, 10, 13cbvrab 2956 . 2
151, 14eqtri 2458 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1550   wceq 1653   wcel 1726   wne 2601  crab 2711  cfv 5457 This theorem is referenced by:  bnj1523  29514 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 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 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 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-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-iota 5421  df-fv 5465
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