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Theorem chvar 1750
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 143 . . 3  |-  ( x  =  y  ->  ( ph  ->  ps ) )
41, 3spim 1731 . 2  |-  ( A. x ph  ->  ps )
5 chvar.3 . 2  |-  ph
64, 5mpg 1444 1  |-  ps
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   F/wnf 1453
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 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-i9 1523  ax-ial 1527
This theorem depends on definitions:  df-bi 116  df-nf 1454
This theorem is referenced by:  csbhypf  3087  opelopabsb  4245  findes  4587  fvmptssdm  5580  dfoprab4f  6172  dom2lem  6750  uzind4s  9549  fsumsplitf  11371
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