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Theorem sbid 1730
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 1660 . . 3  |-  x  =  x
2 sbequ12 1727 . . 3  |-  ( x  =  x  ->  ( ph 
<->  [ x  /  x ] ph ) )
31, 2ax-mp 5 . 2  |-  ( ph  <->  [ x  /  x ] ph )
43bicomi 131 1  |-  ( [ x  /  x ] ph 
<-> 
ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 104   [wsb 1718
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-4 1470  ax-17 1489  ax-i9 1493
This theorem depends on definitions:  df-bi 116  df-sb 1719
This theorem is referenced by:  abid  2103  sbceq1a  2889  sbcid  2895
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