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Theorem vtocle 3134
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 3131 . 2  |-  ( A  e.  _V  ->  ph )
41, 3ax-mp 5 1  |-  ph
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1454    e. wcel 1897   _Vcvv 3056
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-12 1943  ax-ext 2441
This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1457  df-ex 1674  df-sb 1808  df-clab 2448  df-cleq 2454  df-clel 2457  df-v 3058
This theorem is referenced by:  zfrepclf  4534  tz6.12i  5907  eloprabga  6409  cfflb  8714  axcc3  8893  nn0ind-raph  11063  finxpreclem6  31832
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