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Theorem sbidd-misc 42259
Description: An identity theorem for substitution. See sbid 2100. 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 2100 . 2 ([𝑥 / 𝑥]𝜓𝜓)
21imbi2i 325 1 ((𝜑 → [𝑥 / 𝑥]𝜓) ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  [wsb 1867
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-sb 1868
This theorem is referenced by: (None)
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