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Theorem pm13.193 36806
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 2094 . 2  |-  ( x  =  y  ->  ( ph 
<->  [ y  /  x ] ph ) )
21pm5.32ri 648 1  |-  ( (
ph  /\  x  =  y )  <->  ( [
y  /  x ] ph  /\  x  =  y ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 189    /\ wa 375   [wsb 1808
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-12 1944
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1675  df-sb 1809
This theorem is referenced by: (None)
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