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Theorem sbid 1875
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 1662 . . 3  |-  x  =  x
2 sbequ12 1872 . . 3  |-  ( x  =  x  ->  ( ph 
<->  [ x  /  x ] ph ) )
31, 2ax-mp 8 . 2  |-  ( ph  <->  [ x  /  x ] ph )
43bicomi 193 1  |-  ( [ x  /  x ] ph 
<-> 
ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   [wsb 1638
This theorem is referenced by:  abid  2284  sbceq1a  3014  sbcid  3020  csbid  3101  sbidd  28442  sbidd-misc  28443  bnj605  29255
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-sb 1639
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