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Theorem sbid 2255
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]𝜑𝜑)

Proof of Theorem sbid
StepHypRef Expression
1 equid 2011 . 2 𝑥 = 𝑥
2 sbequ12r 2252 . 2 (𝑥 = 𝑥 → ([𝑥 / 𝑥]𝜑𝜑))
31, 2ax-mp 5 1 ([𝑥 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 206  [wsb 2064
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-12 2177
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-sb 2065
This theorem is referenced by:  sbcovOLD  2257  sbco  2512  sbidm  2515  abid  2718  sbceq1a  3799  sbcid  3805  frege58bid  43915  ichid  47438  sbidd  49237  sbidd-misc  49238
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