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Theorem bnj1386 29279
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1386.1
bnj1386.2
bnj1386.3
bnj1386.4
Assertion
Ref Expression
bnj1386
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,,)   (,,)   ()   (,,)

Proof of Theorem bnj1386
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj1386.1 . 2
2 bnj1386.2 . 2
3 bnj1386.3 . 2
4 bnj1386.4 . 2
5 biid 229 . 2
6 eqid 2438 . 2
7 biid 229 . 2
81, 2, 3, 4, 5, 6, 7bnj1385 29278 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550   wceq 1653   wcel 1726  wral 2707   cin 3321  cuni 4017   cdm 4881   cres 4883   wfun 5451 This theorem is referenced by:  bnj1384  29475 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-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 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-eu 2287  df-mo 2288  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-sbc 3164  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-iun 4097  df-br 4216  df-opab 4270  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-res 4893  df-iota 5421  df-fun 5459  df-fv 5465
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