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Theorem ceqsex2v 2896
 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 1619 . 2
2 nfv 1619 . 2
3 ceqsex2v.1 . 2
4 ceqsex2v.2 . 2
5 ceqsex2v.3 . 2
6 ceqsex2v.4 . 2
71, 2, 3, 4, 5, 6ceqsex2 2895 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   w3a 934  wex 1541   wceq 1642   wcel 1710  cvv 2859 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by:  ceqsex3v  2897  ceqsex4v  2898  opksnelsik  4265  sikexlem  4295  br1stg  4730  elswap  4740  brswap2  4860  brsnsi  5773  oqelins4  5794  dmpprod  5840  lecex  6115  addccan2nclem1  6263  nmembers1lem1  6268
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