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Theorem sbequ12r 1873
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 1872 . . 3  |-  ( y  =  x  ->  ( ph 
<->  [ x  /  y ] ph ) )
21bicomd 192 . 2  |-  ( y  =  x  ->  ( [ x  /  y ] ph  <->  ph ) )
32equcoms 1666 1  |-  ( x  =  y  ->  ( [ x  /  y ] ph  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   [wsb 1638
This theorem is referenced by:  sbidm  2038  abbi  2406  findes  4702  opeliunxp  4756  isarep1  5347  axrepndlem1  8230  axrepndlem2  8231  esumcvg  23469  sbidmNEW7  29558
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-sb 1639
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