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Theorem ceqsex2v 3089
 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 1763 . 2
2 nfv 1763 . 2
3 ceqsex2v.1 . 2
4 ceqsex2v.2 . 2
5 ceqsex2v.3 . 2
6 ceqsex2v.4 . 2
71, 2, 3, 4, 5, 6ceqsex2 3088 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   w3a 986   wceq 1446  wex 1665   wcel 1889  cvv 3047 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-11 1922  ax-12 1935  ax-ext 2433 This theorem depends on definitions:  df-bi 189  df-an 373  df-3an 988  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-v 3049 This theorem is referenced by:  ceqsex3v  3090  ceqsex4v  3091  ispos  16204  elfuns  30694  brimg  30716  brapply  30717  brsuccf  30720  brrestrict  30728  dfrdg4  30730  diblsmopel  34751
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