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Theorem sbequ12r 1946
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 1945 . . 3  |-  ( y  =  x  ->  ( ph 
<->  [ x  /  y ] ph ) )
21bicomd 194 . 2  |-  ( y  =  x  ->  ( [ x  /  y ] ph  <->  ph ) )
32equcoms 1694 1  |-  ( x  =  y  ->  ( [ x  /  y ] ph  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178   [wsb 1659
This theorem is referenced by:  sbidm  2161  abbi  2547  findes  4876  opeliunxp  4930  isarep1  5533  axrepndlem1  8468  axrepndlem2  8469  esumcvg  24477  sbidmNEW7  29585
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-sb 1660
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