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Theorem bj-chvarv 34633
Description: Version of chvar 2020 with a dv condition, which does not require ax-13 2006. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-chvarv.1  |-  F/ x ps
bj-chvarv.2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
bj-chvarv.3  |-  ph
Assertion
Ref Expression
bj-chvarv  |-  ps
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)    ps( x, y)

Proof of Theorem bj-chvarv
StepHypRef Expression
1 bj-chvarv.1 . . 3  |-  F/ x ps
2 bj-chvarv.2 . . . 4  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
32biimpd 207 . . 3  |-  ( x  =  y  ->  ( ph  ->  ps ) )
41, 3bj-spimv 34626 . 2  |-  ( A. x ph  ->  ps )
5 bj-chvarv.3 . 2  |-  ph
64, 5mpg 1628 1  |-  ps
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   F/wnf 1624
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-5 1712  ax-6 1755  ax-7 1798  ax-10 1845  ax-12 1862
This theorem depends on definitions:  df-bi 185  df-ex 1621  df-nf 1625
This theorem is referenced by:  bj-chvarvv  34634  bj-axrep2  34722  bj-axrep3  34723
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