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Theorem ceqsexgv 3232
Description: Elimination of an existential quantifier, using implicit substitution. (Contributed by NM, 29-Dec-1996.)
Hypothesis
Ref Expression
ceqsexgv.1
Assertion
Ref Expression
ceqsexgv
Distinct variable groups:   ,   ,

Proof of Theorem ceqsexgv
StepHypRef Expression
1 nfv 1707 . 2
2 ceqsexgv.1 . 2
31, 2ceqsexg 3231 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818
This theorem is referenced by:  ceqsrexv  3233  clel3g  3237  elxp5  6745  xpsnen  7621  isssc  15189  metuel2  21082  isgrpo  25198  ismgmOLD  25322  ceqsex3vOLD  30602  bj-finsumval0  34663  pmapjat1  35577
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-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  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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