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Theorem sbid 2101
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 1863 . 2  |-  x  =  x
2 sbequ12r 2099 . 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 189   [wsb 1805
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-12 1950
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-sb 1806
This theorem is referenced by:  sbco  2261  sbidm  2263  sbal2  2310  abid  2459  sbceq1a  3266  sbcid  3272  frege58bid  36569  sbidd  40946  sbidd-misc  40947
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