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Theorem vtocleg 2712
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 10-Jan-2004.)
Hypothesis
Ref Expression
vtocleg.1  |-  ( x  =  A  ->  ph )
Assertion
Ref Expression
vtocleg  |-  ( A  e.  V  ->  ph )
Distinct variable groups:    x, A    ph, x
Allowed substitution hint:    V( x)

Proof of Theorem vtocleg
StepHypRef Expression
1 elisset 2655 . 2  |-  ( A  e.  V  ->  E. x  x  =  A )
2 vtocleg.1 . . 3  |-  ( x  =  A  ->  ph )
32exlimiv 1545 . 2  |-  ( E. x  x  =  A  ->  ph )
41, 3syl 14 1  |-  ( A  e.  V  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1299   E.wex 1436    e. wcel 1448
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1391  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-ext 2082
This theorem depends on definitions:  df-bi 116  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-v 2643
This theorem is referenced by:  vtocle  2715  spsbc  2873  prexg  4071  funimaexglem  5142  eloprabga  5790  bj-prexg  12690
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