ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbid Unicode version

Theorem sbid 1699
Description: An identity theorem for substitution. Remark 9.1 in [Megill] p. 447 (p. 15 of the preprint). (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbid  |-  ( [ x  /  x ] ph 
<-> 
ph )

Proof of Theorem sbid
StepHypRef Expression
1 equid 1630 . . 3  |-  x  =  x
2 sbequ12 1696 . . 3  |-  ( x  =  x  ->  ( ph 
<->  [ x  /  x ] ph ) )
31, 2ax-mp 7 . 2  |-  ( ph  <->  [ x  /  x ] ph )
43bicomi 130 1  |-  ( [ x  /  x ] ph 
<-> 
ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 103   [wsb 1687
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464
This theorem depends on definitions:  df-bi 115  df-sb 1688
This theorem is referenced by:  abid  2071  sbceq1a  2833  sbcid  2839
  Copyright terms: Public domain W3C validator