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Theorem sbid 1895
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 1818 . . 3  |-  x  =  x
2 sbequ12 1892 . . 3  |-  ( x  =  x  ->  ( ph 
<->  [ x  /  x ] ph ) )
31, 2ax-mp 10 . 2  |-  ( ph  <->  [ x  /  x ] ph )
43bicomi 195 1  |-  ( [ x  /  x ] ph 
<-> 
ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   [wsb 1882
This theorem is referenced by:  abid  2241  sbceq1a  2931  sbcid  2937  csbid  3016  sbidd  26877  sbidd-misc  26878  bnj605  27628
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 1883
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