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Theorem bnj941 28849
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj941.1
Assertion
Ref Expression
bnj941

Proof of Theorem bnj941
StepHypRef Expression
1 bnj941.1 . . . . 5
2 opeq2 3945 . . . . . . 7
32sneqd 3787 . . . . . 6
43uneq2d 3461 . . . . 5
51, 4syl5eq 2448 . . . 4
65fneq1d 5495 . . 3
76imbi2d 308 . 2
8 eqid 2404 . . 3
9 0ex 4299 . . . 4
109elimel 3751 . . 3
118, 10bnj927 28845 . 2
127, 11dedth 3740 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1649   wcel 1721  cvv 2916   cun 3278  c0 3588  cif 3699  csn 3774  cop 3777   csuc 4543   wfn 5408 This theorem is referenced by:  bnj945  28850  bnj910  29025 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-sep 4290  ax-nul 4298  ax-pr 4363  ax-reg 7516 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258  df-mo 2259  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-ral 2671  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-br 4173  df-opab 4227  df-id 4458  df-suc 4547  df-xp 4843  df-rel 4844  df-cnv 4845  df-co 4846  df-dm 4847  df-fun 5415  df-fn 5416
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