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Theorem vtocleg 3127
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 3067 . 2  |-  ( A  e.  V  ->  E. x  x  =  A )
2 vtocleg.1 . . 3  |-  ( x  =  A  ->  ph )
32exlimiv 1741 . 2  |-  ( E. x  x  =  A  ->  ph )
41, 3syl 17 1  |-  ( A  e.  V  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1403   E.wex 1631    e. wcel 1840
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-6 1769  ax-7 1812  ax-12 1876  ax-ext 2378
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1406  df-ex 1632  df-sb 1762  df-clab 2386  df-cleq 2392  df-clel 2395  df-v 3058
This theorem is referenced by:  vtocle  3130  spsbc  3287  prex  4630  avril1  25470  frege58c  35866
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