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Theorem pm13.193 31486
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 2000 . 2  |-  ( x  =  y  ->  ( ph 
<->  [ y  /  x ] ph ) )
21pm5.32ri 636 1  |-  ( (
ph  /\  x  =  y )  <->  ( [
y  /  x ] ph  /\  x  =  y ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 367   [wsb 1747
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-5 1712  ax-6 1755  ax-7 1798  ax-12 1862
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1621  df-sb 1748
This theorem is referenced by: (None)
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