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Theorem sbequ12a 1698
Description: An equality theorem for substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbequ12a  |-  ( x  =  y  ->  ( [ y  /  x ] ph  <->  [ x  /  y ] ph ) )

Proof of Theorem sbequ12a
StepHypRef Expression
1 sbequ12 1696 . 2  |-  ( x  =  y  ->  ( ph 
<->  [ y  /  x ] ph ) )
2 sbequ12 1696 . . 3  |-  ( y  =  x  ->  ( ph 
<->  [ x  /  y ] ph ) )
32equcoms 1636 . 2  |-  ( x  =  y  ->  ( ph 
<->  [ x  /  y ] ph ) )
41, 3bitr3d 188 1  |-  ( x  =  y  ->  ( [ y  /  x ] ph  <->  [ x  /  y ] ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   [wsb 1687
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-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464
This theorem depends on definitions:  df-bi 115  df-sb 1688
This theorem is referenced by: (None)
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