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Theorem bj-chvarvv 33770
Description: Version of chvarv 1983 with a dv condition, which does not require ax-13 1968. (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 1683 . 2  |-  F/ x ps
2 bj-chvarvv.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
3 bj-chvarvv.2 . 2  |-  ph
41, 2, 3bj-chvarv 33769 1  |-  ps
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-12 1803
This theorem depends on definitions:  df-bi 185  df-ex 1597  df-nf 1600
This theorem is referenced by:  bj-axext3  33836  bj-axrep1  33856  bj-axsep2  33975
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