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Theorem pm13.193 27010
Description: Theorem *13.193 in [WhiteheadRussell] p. 179. (Contributed by Andrew Salmon, 3-Jun-2011.)
Assertion
Ref Expression
pm13.193  |-  ( (
ph  /\  x  =  y )  <->  ( [
y  /  x ] ph  /\  x  =  y ) )

Proof of Theorem pm13.193
StepHypRef Expression
1 sbequ12 1861 . 2  |-  ( x  =  y  ->  ( ph 
<->  [ y  /  x ] ph ) )
21pm5.32ri 621 1  |-  ( (
ph  /\  x  =  y )  <->  ( [
y  /  x ] ph  /\  x  =  y ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360   [wsb 1631
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-11 1716
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1530  df-sb 1632
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