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Theorem bi2imp 39188
Description: Importation inference similar to imp 444, except both implications of the hypothesis are biconditionals. (Contributed by Alan Sare, 6-Nov-2017.)
Hypothesis
Ref Expression
bi2imp.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
bi2imp ((𝜑𝜓) → 𝜒)

Proof of Theorem bi2imp
StepHypRef Expression
1 bi2imp.1 . . 3 (𝜑 ↔ (𝜓𝜒))
21biimpi 206 . 2 (𝜑 → (𝜓𝜒))
32biimpa 502 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 383
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 197  df-an 385
This theorem is referenced by: (None)
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