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Theorem ceqsex2v 3148
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:   , ,   , ,   ,   ,

Proof of Theorem ceqsex2v
StepHypRef Expression
1 nfv 1707 . 2
2 nfv 1707 . 2
3 ceqsex2v.1 . 2
4 ceqsex2v.2 . 2
5 ceqsex2v.3 . 2
6 ceqsex2v.4 . 2
71, 2, 3, 4, 5, 6ceqsex2 3147 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  =wceq 1395  E.wex 1612  e.wcel 1818   cvv 3109
This theorem is referenced by:  ceqsex3v  3149  ceqsex4v  3150  ispos  15576  elfuns  29565  brimg  29587  brapply  29588  brsuccf  29591  brrestrict  29599  dfrdg4  29600  diblsmopel  36898
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
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