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Theorem sbid 2239
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 2007 . 2 𝑥 = 𝑥
2 sbequ12r 2236 . 2 (𝑥 = 𝑥 → ([𝑥 / 𝑥]𝜑𝜑))
31, 2ax-mp 5 1 ([𝑥 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  [wsb 2059
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-12 2163
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774  df-sb 2060
This theorem is referenced by:  sbcov  2240  sbco  2498  sbidm  2501  abid  2705  sbceq1a  3781  sbcid  3787  frege58bid  43167  ichid  46629  sbidd  47975  sbidd-misc  47976
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