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Theorem sbidd-misc 28180
Description: An identity theorem for substitution. See sbid 1943. 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 1943 . 2  |-  ( [ x  /  x ] ps 
<->  ps )
21imbi2i 304 1  |-  ( (
ph  ->  [ x  /  x ] ps )  <->  ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   [wsb 1655
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-11 1757
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-sb 1656
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