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Theorem nfbii 1362
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 1359 . . . 4  |-  ( A. x ph  <->  A. x ps )
31, 2imbi12i 228 . . 3  |-  ( (
ph  ->  A. x ph )  <->  ( ps  ->  A. x ps ) )
43albii 1359 . 2  |-  ( A. x ( ph  ->  A. x ph )  <->  A. x
( ps  ->  A. x ps ) )
5 df-nf 1350 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
6 df-nf 1350 . 2  |-  ( F/ x ps  <->  A. x
( ps  ->  A. x ps ) )
74, 5, 63bitr4i 201 1  |-  ( F/ x ph  <->  F/ x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98   A.wal 1241   F/wnf 1349
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338
This theorem depends on definitions:  df-bi 110  df-nf 1350
This theorem is referenced by:  nfxfr  1363  nfxfrd  1364  nfsb  1822  nfsbt  1850  hbsbd  1858  sbal1yz  1877  dvelimALT  1886  dvelimfv  1887  dvelimor  1894  nfeudv  1915  nfeuv  1918  nfceqi  2174  nfreudxy  2483  dfnfc2  3598
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