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Theorem ceqsex2v 2993
 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 1629 . 2
2 nfv 1629 . 2
3 ceqsex2v.1 . 2
4 ceqsex2v.2 . 2
5 ceqsex2v.3 . 2
6 ceqsex2v.4 . 2
71, 2, 3, 4, 5, 6ceqsex2 2992 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   w3a 936  wex 1550   wceq 1652   wcel 1725  cvv 2956 This theorem is referenced by:  ceqsex3v  2994  ceqsex4v  2995  ispos  14404  elfuns  25760  brimg  25782  brapply  25783  brsuccf  25786  brrestrict  25794  dfrdg4  25795  diblsmopel  31969 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-v 2958
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