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Theorem sbequ12aOLD 1939
Description: Obsolete proof of sbequ12a 1938 as of 23-Jun-2019. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sbequ12aOLD  |-  ( x  =  y  ->  ( [ y  /  x ] ph  <->  [ x  /  y ] ph ) )

Proof of Theorem sbequ12aOLD
StepHypRef Expression
1 sbequ12 1936 . 2  |-  ( x  =  y  ->  ( ph 
<->  [ y  /  x ] ph ) )
2 sbequ12 1936 . . 3  |-  ( y  =  x  ->  ( ph 
<->  [ x  /  y ] ph ) )
32equcoms 1733 . 2  |-  ( x  =  y  ->  ( ph 
<->  [ x  /  y ] ph ) )
41, 3bitr3d 255 1  |-  ( x  =  y  ->  ( [ y  /  x ] ph  <->  [ x  /  y ] ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   [wsb 1700
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-12 1792
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1587  df-sb 1701
This theorem is referenced by: (None)
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