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Theorem nfbii 1450
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 1447 . . . 4  |-  ( A. x ph  <->  A. x ps )
31, 2imbi12i 238 . . 3  |-  ( (
ph  ->  A. x ph )  <->  ( ps  ->  A. x ps ) )
43albii 1447 . 2  |-  ( A. x ( ph  ->  A. x ph )  <->  A. x
( ps  ->  A. x ps ) )
5 df-nf 1438 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
6 df-nf 1438 . 2  |-  ( F/ x ps  <->  A. x
( ps  ->  A. x ps ) )
74, 5, 63bitr4i 211 1  |-  ( F/ x ph  <->  F/ x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1330   F/wnf 1437
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426
This theorem depends on definitions:  df-bi 116  df-nf 1438
This theorem is referenced by:  nfxfr  1451  nfxfrd  1452  nfsb  1920  nfsbt  1950  hbsbd  1958  sbal1yz  1977  dvelimALT  1986  dvelimfv  1987  dvelimor  1994  nfeudv  2015  nfeuv  2018  nfceqi  2278  nfreudxy  2607  dfnfc2  3761
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