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Theorem bj-chvarvv 31067
Description: Version of chvarv 2070 with a dv condition, which does not require ax-13 2055. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-chvarvv.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
bj-chvarvv.2  |-  ph
Assertion
Ref Expression
bj-chvarvv  |-  ps
Distinct variable groups:    x, y    ps, x
Allowed substitution hints:    ph( x, y)    ps( y)

Proof of Theorem bj-chvarvv
StepHypRef Expression
1 nfv 1754 . 2  |-  F/ x ps
2 bj-chvarvv.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
3 bj-chvarvv.2 . 2  |-  ph
41, 2, 3bj-chvarv 31066 1  |-  ps
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-12 1907
This theorem depends on definitions:  df-bi 188  df-ex 1660  df-nf 1664
This theorem is referenced by:  bj-axext3  31134  bj-axrep1  31154  bj-axsep2  31278
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