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Theorem nfbii 1692
Description: Equality theorem for not-free. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfbii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
nfbii  |-  ( F/ x ph  <->  F/ x ps )

Proof of Theorem nfbii
StepHypRef Expression
1 nfbii.1 . . . 4  |-  ( ph  <->  ps )
21albii 1688 . . . 4  |-  ( A. x ph  <->  A. x ps )
31, 2imbi12i 328 . . 3  |-  ( (
ph  ->  A. x ph )  <->  ( ps  ->  A. x ps ) )
43albii 1688 . 2  |-  ( A. x ( ph  ->  A. x ph )  <->  A. x
( ps  ->  A. x ps ) )
5 df-nf 1665 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
6 df-nf 1665 . 2  |-  ( F/ x ps  <->  A. x
( ps  ->  A. x ps ) )
74, 5, 63bitr4i 281 1  |-  ( 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
This theorem depends on definitions:  df-bi 189  df-nf 1665
This theorem is referenced by:  nfxfr  1693  nfxfrd  1694  dvelimhw  2012  nfeqf1  2099  nfceqiOLD  2582  dfnfc2  4236  bj-nfcf  31494  iunconlem2  37241
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