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Theorem bnj1185 29165
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1185.1
Assertion
Ref Expression
bnj1185
Distinct variable groups:   ,,,   ,,,   ,,,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem bnj1185
StepHypRef Expression
1 bnj1185.1 . . 3
2 breq1 4215 . . . . . 6
32notbid 286 . . . . 5
43cbvralv 2932 . . . 4
54rexbii 2730 . . 3
61, 5sylib 189 . 2
7 eleq1 2496 . . . . 5
8 breq2 4216 . . . . . . 7
98notbid 286 . . . . . 6
109ralbidv 2725 . . . . 5
117, 10anbi12d 692 . . . 4
1211cbvexv 1985 . . 3
13 df-rex 2711 . . 3
14 df-rex 2711 . . 3
1512, 13, 143bitr4ri 270 . 2
166, 15sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wex 1550   wcel 1725  wral 2705  wrex 2706   class class class wbr 4212 This theorem is referenced by:  bnj1190  29377  bnj1189  29378 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-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213
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