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Theorem sbid 2086
Description: An identity theorem for substitution. Remark 9.1 in [Megill] p. 447 (p. 15 of the preprint). (Contributed by NM, 26-May-1993.) (Proof shortened by Wolf Lammen, 30-Sep-2018.)
Assertion
Ref Expression
sbid  |-  ( [ x  /  x ] ph 
<-> 
ph )

Proof of Theorem sbid
StepHypRef Expression
1 equid 1855 . 2  |-  x  =  x
2 sbequ12r 2084 . 2  |-  ( x  =  x  ->  ( [ x  /  x ] ph  <->  ph ) )
31, 2ax-mp 5 1  |-  ( [ x  /  x ] ph 
<-> 
ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 188   [wsb 1797
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-12 1933
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-sb 1798
This theorem is referenced by:  sbco  2241  sbidm  2243  sbal2  2290  abid  2439  sbceq1a  3278  sbcid  3284  frege58bid  36498  sbidd  40491  sbidd-misc  40492
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