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Theorem sbequ12a 1999
Description: An equality theorem for substitution. (Contributed by NM, 2-Jun-1993.) (Proof shortened by Wolf Lammen, 23-Jun-2019.)
Assertion
Ref Expression
sbequ12a  |-  ( x  =  y  ->  ( [ y  /  x ] ph  <->  [ x  /  y ] ph ) )

Proof of Theorem sbequ12a
StepHypRef Expression
1 sbequ12r 1998 . 2  |-  ( x  =  y  ->  ( [ x  /  y ] ph  <->  ph ) )
2 sbequ12 1997 . 2  |-  ( x  =  y  ->  ( ph 
<->  [ y  /  x ] ph ) )
31, 2bitr2d 254 1  |-  ( x  =  y  ->  ( [ y  /  x ] ph  <->  [ x  /  y ] ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   [wsb 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-12 1859
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618  df-sb 1745
This theorem is referenced by:  sbco3  2162  sb9  2171
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