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Theorem chvar 1757
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 144 . . 3  |-  ( x  =  y  ->  ( ph  ->  ps ) )
41, 3spim 1738 . 2  |-  ( A. x ph  ->  ps )
5 chvar.3 . 2  |-  ph
64, 5mpg 1451 1  |-  ps
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 105   F/wnf 1460
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-i9 1530  ax-ial 1534
This theorem depends on definitions:  df-bi 117  df-nf 1461
This theorem is referenced by:  csbhypf  3095  opelopabsb  4260  findes  4602  fvmptssdm  5600  dfoprab4f  6193  dom2lem  6771  uzind4s  9588  fsumsplitf  11411
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