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Theorem nfbii 1575
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 1572 . . . 4  |-  ( A. x ph  <->  A. x ps )
31, 2imbi12i 317 . . 3  |-  ( (
ph  ->  A. x ph )  <->  ( ps  ->  A. x ps ) )
43albii 1572 . 2  |-  ( A. x ( ph  ->  A. x ph )  <->  A. x
( ps  ->  A. x ps ) )
5 df-nf 1551 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
6 df-nf 1551 . 2  |-  ( F/ x ps  <->  A. x
( ps  ->  A. x ps ) )
74, 5, 63bitr4i 269 1  |-  ( F/ x ph  <->  F/ x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1546   F/wnf 1550
This theorem is referenced by:  nfxfr  1576  nfxfrd  1577  dvelimhw  1872  dvelimh  2015  nfceqi  2536  dfnfc2  3993  nfsb4tw2AUXOLD7  29430  sbcomOLD7  29439  sb9iOLD7  29442
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563
This theorem depends on definitions:  df-bi 178  df-nf 1551
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