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Theorem sbid 1180
Description: An identity theorem for substitution. Remark 9.1 in [Megill] p. 447 (p. 15 of the preprint).
Assertion
Ref Expression
sbid |- ([x / x]ph <-> ph)
Proof of Theorem sbid
StepHypRef Expression
1 equid 1122 . . 3 |- x = x
2 sbequ12 1177 . . 3 |- (x = x -> (ph <-> [x / x]ph))
31, 2ax-mp 7 . 2 |- (ph <-> [x / x]ph)
43bicomi 172 1 |- ([x / x]ph <-> ph)
Colors of variables: wff set class
Syntax hints:   <-> wb 146  [wsbc 1166
This theorem is referenced by:  abid 1458  sbceq1a 1934  csbid 1995
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-12 965  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119
This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168
Copyright terms: Public domain