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Theorem sbid 1704
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 1634 . . 3  |-  x  =  x
2 sbequ12 1701 . . 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 1692
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 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-4 1445  ax-17 1464  ax-i9 1468
This theorem depends on definitions:  df-bi 115  df-sb 1693
This theorem is referenced by:  abid  2076  sbceq1a  2849  sbcid  2855
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