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Theorem sbidd-misc 27322
Description: An identity theorem for substitution. See sbid 1896. 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 1896 . . 3  |-  ( [ x  /  x ] ps 
<->  ps )
21a1i 12 . 2  |-  ( ph  ->  ( [ x  /  x ] ps  <->  ps )
)
32pm5.74i 238 1  |-  ( (
ph  ->  [ x  /  x ] ps )  <->  ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   [wsb 1883
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-12o 1664  ax-9 1684  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-sb 1884
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