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Theorem ceqsex2v 2651
 Description: Elimination of two existential quantifiers, using implicit substitution. (Contributed by Scott Fenton, 7-Jun-2006.)
Hypotheses
Ref Expression
ceqsex2v.1
ceqsex2v.2
ceqsex2v.3
ceqsex2v.4
Assertion
Ref Expression
ceqsex2v
Distinct variable groups:   ,,   ,,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem ceqsex2v
StepHypRef Expression
1 nfv 1462 . 2
2 nfv 1462 . 2
3 ceqsex2v.1 . 2
4 ceqsex2v.2 . 2
5 ceqsex2v.3 . 2
6 ceqsex2v.4 . 2
71, 2, 3, 4, 5, 6ceqsex2 2650 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   w3a 920   wceq 1285  wex 1422   wcel 1434  cvv 2612 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-3an 922  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-v 2614 This theorem is referenced by:  ceqsex3v  2652  ceqsex4v  2653
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