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Theorem sbid 2254
 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 2019 . 2 𝑥 = 𝑥
2 sbequ12r 2251 . 2 (𝑥 = 𝑥 → ([𝑥 / 𝑥]𝜑𝜑))
31, 2ax-mp 5 1 ([𝑥 / 𝑥]𝜑𝜑)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209  [wsb 2069 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-12 2175 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070 This theorem is referenced by:  sbcov  2255  sbco  2526  sbidm  2529  sbal2OLD  2550  abid  2780  sbceq1a  3733  sbcid  3739  frege58bid  40774  ichid  44136  sbidd  45410  sbidd-misc  45411
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