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Theorem bnj1534 32689
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:   , , ,   , ,   , , ,

Proof of Theorem bnj1534
StepHypRef Expression
1 bnj1534.1 . 2
2 nfcv 2616 . . 3
3 nfcv 2616 . . 3
4 nfv 1674 . . 3
5 bnj1534.2 . . . . . 6
65nfcii 2606 . . . . 5
7 nfcv 2616 . . . . 5
86, 7nffv 5820 . . . 4
9 nfcv 2616 . . . 4
108, 9nfne 2784 . . 3
11 fveq2 5813 . . . 4
12 fveq2 5813 . . . 4
1311, 12neeq12d 2732 . . 3
142, 3, 4, 10, 13cbvrab 3079 . 2
151, 14eqtri 2483 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1368  =wceq 1370  e.wcel 1758  =/=wne 2648  {crab 2804  `cfv 5537
This theorem is referenced by:  bnj1523  32905
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2805  df-rex 2806  df-rab 2809  df-v 3083  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3752  df-if 3906  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4209  df-br 4410  df-iota 5500  df-fv 5545
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