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Theorem sbidd-misc 28443
Description: An identity theorem for substitution. See sbid 1875. See Remark 9.1 in [Megill] p. 447 (p. 15 of the preprint). (Contributed by DAW, 18-Feb-2017.)
Assertion
Ref Expression
sbidd-misc  |-  ( (
ph  ->  [ x  /  x ] ps )  <->  ( ph  ->  ps ) )

Proof of Theorem sbidd-misc
StepHypRef Expression
1 sbid 1875 . . 3  |-  ( [ x  /  x ] ps 
<->  ps )
21a1i 10 . 2  |-  ( ph  ->  ( [ x  /  x ] ps  <->  ps )
)
32pm5.74i 236 1  |-  ( (
ph  ->  [ x  /  x ] ps )  <->  ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   [wsb 1638
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-sb 1639
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