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Theorem sbid 2247
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 2015 . 2 𝑥 = 𝑥
2 sbequ12r 2244 . 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 2067
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 1913  ax-6 1971  ax-7 2011  ax-12 2171
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1782  df-sb 2068
This theorem is referenced by:  sbcov  2248  sbco  2506  sbidm  2509  abid  2713  sbceq1a  3787  sbcid  3793  frege58bid  42638  ichid  46105  sbidd  47716  sbidd-misc  47717
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