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Theorem vtocleg 3189
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 21-Jun-1993.)
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 3129 . 2  |-  ( A  e.  V  ->  E. x  x  =  A )
2 vtocleg.1 . . 3  |-  ( x  =  A  ->  ph )
32exlimiv 1698 . 2  |-  ( E. x  x  =  A  ->  ph )
41, 3syl 16 1  |-  ( A  e.  V  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1379   E.wex 1596    e. wcel 1767
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-12 1803  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-v 3120
This theorem is referenced by:  vtocle  3192  spsbc  3349  prex  4695  avril1  24994
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