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Theorem vtocle 3167
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 3164 . 2  |-  ( A  e.  _V  ->  ph )
41, 3ax-mp 5 1  |-  ph
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1381    e. wcel 1802   _Vcvv 3093
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-12 1838  ax-ext 2419
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1384  df-ex 1598  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-v 3095
This theorem is referenced by:  zfrepclf  4551  tz6.12i  5873  eloprabga  6371  cfflb  8639  axcc3  8818  nn0ind-raph  10966
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