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Theorem bj-cbvalvv 31400
Description: Version of cbvalv 2129 with a dv condition, which does not require ax-13 2104. UPDATE: this is cbvalvw 1886 (which is proved with fewer axioms). (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-cbvalvv.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
bj-cbvalvv  |-  ( A. x ph  <->  A. y ps )
Distinct variable groups:    x, y    ph, y    ps, x
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem bj-cbvalvv
StepHypRef Expression
1 nfv 1769 . 2  |-  F/ y
ph
2 nfv 1769 . 2  |-  F/ x ps
3 bj-cbvalvv.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
41, 2, 3cbvalv1 2083 1  |-  ( A. x ph  <->  A. y ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 189   A.wal 1450
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676
This theorem is referenced by:  bj-zfpow  31476  bj-nfcjust  31527
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