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Theorem sbidd-misc 43372
Description: An identity theorem for substitution. See sbid 2289. See Remark 9.1 in [Megill] p. 447 (p. 15 of the preprint). (Contributed by DAW, 18-Feb-2017.)
Assertion
Ref Expression
sbidd-misc ((𝜑 → [𝑥 / 𝑥]𝜓) ↔ (𝜑𝜓))

Proof of Theorem sbidd-misc
StepHypRef Expression
1 sbid 2289 . 2 ([𝑥 / 𝑥]𝜓𝜓)
21imbi2i 328 1 ((𝜑 → [𝑥 / 𝑥]𝜓) ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198  [wsb 2067
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-12 2220
This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1879  df-sb 2068
This theorem is referenced by: (None)
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