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Theorem bj-drnf2v 34749
Description: Version of drnf2 2076 with a dv condition, which does not require ax-13 2004. Could be labelled "nfbidv". (Contributed by BJ, 17-Jun-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-drnf2v.1  |-  ( A. x  x  =  y  ->  ( ph  <->  ps )
)
Assertion
Ref Expression
bj-drnf2v  |-  ( A. x  x  =  y  ->  ( F/ z ph  <->  F/ z ps ) )
Distinct variable group:    x, y, z
Allowed substitution hints:    ph( x, y, z)    ps( x, y, z)

Proof of Theorem bj-drnf2v
StepHypRef Expression
1 nfv 1712 . 2  |-  F/ z A. x  x  =  y
2 bj-drnf2v.1 . 2  |-  ( A. x  x  =  y  ->  ( ph  <->  ps )
)
31, 2nfbidf 1892 1  |-  ( A. x  x  =  y  ->  ( F/ z ph  <->  F/ z ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1396   F/wnf 1621
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-12 1859
This theorem depends on definitions:  df-bi 185  df-ex 1618  df-nf 1622
This theorem is referenced by: (None)
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