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Theorem sbequ12a 1947
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 1946 . 2  |-  ( x  =  y  ->  ( [ x  /  y ] ph  <->  ph ) )
2 sbequ12 1945 . 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 1702
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-sb 1703
This theorem is referenced by:  sbco3  2121  sbco3OLD  2122  sb9  2133
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