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Theorem bi1imp 37605
Description: Importation inference similar to imp 443, except the outermost implication of the hypothesis is a biconditional. (Contributed by Alan Sare, 6-Nov-2017.)
Hypothesis
Ref Expression
bi1imp.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
bi1imp ((𝜑𝜓) → 𝜒)

Proof of Theorem bi1imp
StepHypRef Expression
1 bi1imp.1 . . 3 (𝜑 ↔ (𝜓𝜒))
21biimpi 204 . 2 (𝜑 → (𝜓𝜒))
32imp 443 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wa 382
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 195  df-an 384
This theorem is referenced by: (None)
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