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Theorem nfbii 1407
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 1404 . . . 4  |-  ( A. x ph  <->  A. x ps )
31, 2imbi12i 237 . . 3  |-  ( (
ph  ->  A. x ph )  <->  ( ps  ->  A. x ps ) )
43albii 1404 . 2  |-  ( A. x ( ph  ->  A. x ph )  <->  A. x
( ps  ->  A. x ps ) )
5 df-nf 1395 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
6 df-nf 1395 . 2  |-  ( F/ x ps  <->  A. x
( ps  ->  A. x ps ) )
74, 5, 63bitr4i 210 1  |-  ( F/ x ph  <->  F/ x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1287   F/wnf 1394
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383
This theorem depends on definitions:  df-bi 115  df-nf 1395
This theorem is referenced by:  nfxfr  1408  nfxfrd  1409  nfsb  1870  nfsbt  1898  hbsbd  1906  sbal1yz  1925  dvelimALT  1934  dvelimfv  1935  dvelimor  1942  nfeudv  1963  nfeuv  1966  nfceqi  2224  nfreudxy  2540  dfnfc2  3671
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