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Theorem bnj919 29136
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj919.1
bnj919.2
bnj919.3
bnj919.4
bnj919.5
Assertion
Ref Expression
bnj919
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   ()   ()

Proof of Theorem bnj919
StepHypRef Expression
1 bnj919.4 . 2
2 bnj919.1 . . 3
32sbcbii 3216 . 2
4 bnj919.5 . . 3
5 df-bnj17 29051 . . . . 5
6 nfv 1629 . . . . . . 7
7 nfv 1629 . . . . . . 7
8 bnj919.2 . . . . . . . 8
9 nfsbc1v 3180 . . . . . . . 8
108, 9nfxfr 1579 . . . . . . 7
116, 7, 10nf3an 1849 . . . . . 6
12 bnj919.3 . . . . . . 7
13 nfsbc1v 3180 . . . . . . 7
1412, 13nfxfr 1579 . . . . . 6
1511, 14nfan 1846 . . . . 5
165, 15nfxfr 1579 . . . 4
17 eleq1 2496 . . . . . 6
18 fneq2 5535 . . . . . . 7
19 sbceq1a 3171 . . . . . . . 8
2019, 8syl6bbr 255 . . . . . . 7
21 sbceq1a 3171 . . . . . . . 8
2221, 12syl6bbr 255 . . . . . . 7
2318, 20, 223anbi123d 1254 . . . . . 6
2417, 23anbi12d 692 . . . . 5
25 bnj252 29067 . . . . 5
26 bnj252 29067 . . . . 5
2724, 25, 263bitr4g 280 . . . 4
2816, 27sbciegf 3192 . . 3
294, 28ax-mp 8 . 2
301, 3, 293bitri 263 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725  cvv 2956  wsbc 3161   wfn 5449   w-bnj17 29050 This theorem is referenced by:  bnj910  29319  bnj999  29328  bnj907  29336 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sbc 3162  df-fn 5457  df-bnj17 29051
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