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Theorem ceqsex3vOLD 30850
Description: Version of ceqsexv 3146 with an antecedent instead of a hypothesis. (Use ceqsexgv 3232 instead of this one. --NM 13-Aug-11) (Contributed by Rodolfo Medina, 19-Oct-2010.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ceqsex3v.1OLD  |-  ( x  =  A  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
ceqsex3vOLD  |-  ( A  e.  _V  ->  ( E. x ( x  =  A  /\  ph )  <->  ps ) )
Distinct variable groups:    x, A    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem ceqsex3vOLD
StepHypRef Expression
1 ceqsex3v.1OLD . 2  |-  ( x  =  A  ->  ( ph 
<->  ps ) )
21ceqsexgv 3232 1  |-  ( A  e.  _V  ->  ( E. x ( x  =  A  /\  ph )  <->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369    = wceq 1395   E.wex 1613    e. wcel 1819   _Vcvv 3109
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-12 1855  ax-13 2000  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
This theorem is referenced by: (None)
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