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Theorem vtocle 2734
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993.)
Hypotheses
Ref Expression
vtocle.1  |-  A  e. 
_V
vtocle.2  |-  ( x  =  A  ->  ph )
Assertion
Ref Expression
vtocle  |-  ph
Distinct variable groups:    x, A    ph, x

Proof of Theorem vtocle
StepHypRef Expression
1 vtocle.1 . 2  |-  A  e. 
_V
2 vtocle.2 . . 3  |-  ( x  =  A  ->  ph )
32vtocleg 2731 . 2  |-  ( A  e.  _V  ->  ph )
41, 3ax-mp 5 1  |-  ph
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1316    e. wcel 1465   _Vcvv 2660
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-v 2662
This theorem is referenced by:  repizf2  4056  nn0ind-raph  9136
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