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Theorem chvar 1684
Description: Implicit substitution of  y for  x into a theorem. (Contributed by Raph Levien, 9-Jul-2003.) (Revised by Mario Carneiro, 3-Oct-2016.)
Hypotheses
Ref Expression
chvar.1  |-  F/ x ps
chvar.2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
chvar.3  |-  ph
Assertion
Ref Expression
chvar  |-  ps

Proof of Theorem chvar
StepHypRef Expression
1 chvar.1 . . 3  |-  F/ x ps
2 chvar.2 . . . 4  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
32biimpd 142 . . 3  |-  ( x  =  y  ->  ( ph  ->  ps ) )
41, 3spim 1670 . 2  |-  ( A. x ph  ->  ps )
5 chvar.3 . 2  |-  ph
64, 5mpg 1383 1  |-  ps
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   F/wnf 1392
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-i9 1466  ax-ial 1470
This theorem depends on definitions:  df-bi 115  df-nf 1393
This theorem is referenced by:  csbhypf  2955  opelopabsb  4061  findes  4391  fvmptssdm  5350  dfoprab4f  5920  dom2lem  6441  uzind4s  9010
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