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Theorem bnj1383 29428
 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 239 . 2
5 biid 239 . 2
6 biid 239 . 2
71, 2, 3, 4, 5, 6bnj1379 29427 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   w3a 982   wceq 1437   wcel 1867  wral 2773   cin 3432  cop 3999  cuni 4213   cdm 4845   cres 4847   wfun 5586 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-9 1871  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398  ax-sep 4539  ax-nul 4547  ax-pr 4652 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-eu 2267  df-mo 2268  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-ral 2778  df-rex 2779  df-rab 2782  df-v 3080  df-sbc 3297  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4214  df-iun 4295  df-br 4418  df-opab 4476  df-id 4760  df-xp 4851  df-rel 4852  df-cnv 4853  df-co 4854  df-dm 4855  df-res 4857  df-iota 5556  df-fun 5594  df-fv 5600 This theorem is referenced by:  bnj1385  29429  bnj60  29656
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