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Theorem sbequ12r 2094
Description: An equality theorem for substitution. (Contributed by NM, 6-Oct-2004.) (Proof shortened by Andrew Salmon, 21-Jun-2011.)
Assertion
Ref Expression
sbequ12r  |-  ( x  =  y  ->  ( [ x  /  y ] ph  <->  ph ) )

Proof of Theorem sbequ12r
StepHypRef Expression
1 sbequ12 2093 . . 3  |-  ( y  =  x  ->  ( ph 
<->  [ x  /  y ] ph ) )
21bicomd 206 . 2  |-  ( y  =  x  ->  ( [ x  /  y ] ph  <->  ph ) )
32equcoms 1874 1  |-  ( x  =  y  ->  ( [ x  /  y ] ph  <->  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 189   [wsb 1807
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-12 1943
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1674  df-sb 1808
This theorem is referenced by:  sbequ12a  2095  sbid  2096  sb5rf  2261  sb6rf  2262  2sb5rf  2290  2sb6rf  2291  opeliunxp  4904  isarep1  5683  findes  6749  axrepndlem1  9042  axrepndlem2  9043  nn0min  28432  esumcvg  28955  bj-abbi  31434  bj-sbidmOLD  31490  wl-nfs1t  31915  wl-sb6rft  31921  wl-equsb4  31929  wl-ax11-lem5  31963  sbcalf  32396  sbcexf  32397  opeliun2xp  40386
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