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Theorem bnj1383 29205
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1383.1
bnj1383.2
bnj1383.3
Assertion
Ref Expression
bnj1383
Distinct variable groups:   ,,   ,
Allowed substitution hints:   ()   (,)   (,)

Proof of Theorem bnj1383
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bnj1383.1 . 2
2 bnj1383.2 . 2
3 bnj1383.3 . 2
4 biid 229 . 2
5 biid 229 . 2
6 biid 229 . 2
71, 2, 3, 4, 5, 6bnj1379 29204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937   wceq 1653   wcel 1726  wral 2707   cin 3321  cop 3819  cuni 4017   cdm 4880   cres 4882   wfun 5450 This theorem is referenced by:  bnj1385  29206  bnj60  29433 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 4332  ax-nul 4340  ax-pr 4405 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 4215  df-opab 4269  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-res 4892  df-iota 5420  df-fun 5458  df-fv 5464
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