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Theorem sbequ12r 1746
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 1745 . . 3  |-  ( y  =  x  ->  ( ph 
<->  [ x  /  y ] ph ) )
21bicomd 140 . 2  |-  ( y  =  x  ->  ( [ x  /  y ] ph  <->  ph ) )
32equcoms 1685 1  |-  ( x  =  y  ->  ( [ x  /  y ] ph  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   [wsb 1736
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-4 1488  ax-17 1507  ax-i9 1511
This theorem depends on definitions:  df-bi 116  df-sb 1737
This theorem is referenced by:  abbi  2254  findes  4524  opeliunxp  4601  isarep1  5216  bezoutlemmain  11720
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