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Theorem chvarvv 1880
Description: Version of chvarv 1909 with a disjoint variable condition. (Contributed by BJ, 31-May-2019.)
Hypotheses
Ref Expression
chvarvv.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
chvarvv.2  |-  ph
Assertion
Ref Expression
chvarvv  |-  ps
Distinct variable groups:    x, y    ps, x
Allowed substitution hints:    ph( x, y)    ps( y)

Proof of Theorem chvarvv
StepHypRef Expression
1 chvarvv.1 . . 3  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
21spvv 1879 . 2  |-  ( A. x ph  ->  ps )
3 chvarvv.2 . 2  |-  ph
42, 3mpg 1427 1  |-  ps
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104
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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by:  prodfdivap  11323
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