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Theorem nfbii2 32322
Description: Equality deduction for not-freeness. (Contributed by Giovanni Mascellani, 10-Apr-2018.)
Assertion
Ref Expression
nfbii2  |-  ( A. x ( ph  <->  ps )  ->  ( F/ x ph  <->  F/ x ps ) )

Proof of Theorem nfbii2
StepHypRef Expression
1 nfa1 1953 . 2  |-  F/ x A. x ( ph  <->  ps )
2 sp 1911 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  ps )
)
31, 2nfbidf 1939 1  |-  ( A. x ( ph  <->  ps )  ->  ( F/ x ph  <->  F/ x ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 188   A.wal 1436   F/wnf 1664
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-12 1906
This theorem depends on definitions:  df-bi 189  df-ex 1661  df-nf 1665
This theorem is referenced by: (None)
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