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Theorem sbequ12r 2058
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 2057 . . 3  |-  ( y  =  x  ->  ( ph 
<->  [ x  /  y ] ph ) )
21bicomd 204 . 2  |-  ( y  =  x  ->  ( [ x  /  y ] ph  <->  ph ) )
32equcoms 1849 1  |-  ( x  =  y  ->  ( [ x  /  y ] ph  <->  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187   [wsb 1790
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-12 1909
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-sb 1791
This theorem is referenced by:  sbequ12a  2059  sbid  2060  sb5rf  2227  sb6rf  2228  2sb5rf  2257  2sb6rf  2258  opeliunxp  4848  isarep1  5623  findes  6681  axrepndlem1  8968  axrepndlem2  8969  nn0min  28335  esumcvg  28859  bj-abbi  31301  bj-sbidmOLD  31357  wl-nfs1t  31778  wl-sb6rft  31784  wl-equsb4  31792  wl-ax11-lem5  31826  sbcalf  32259  sbcexf  32260  opeliun2xp  39707
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