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Theorem bnj1386 33993
 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 236 . 2
6 eqid 2457 . 2
7 biid 236 . 2
81, 2, 3, 4, 5, 6, 7bnj1385 33992 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1393   wceq 1395   wcel 1819  wral 2807   cin 3470  cuni 4251   cdm 5008   cres 5010   wfun 5588 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  df-mo 2288  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-iun 4334  df-br 4457  df-opab 4516  df-id 4804  df-xp 5014  df-rel 5015  df-cnv 5016  df-co 5017  df-dm 5018  df-res 5020  df-iota 5557  df-fun 5596  df-fv 5602 This theorem is referenced by:  bnj1384  34189
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