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Theorem bi13imp2 39016
Description: Similar to 3imp 1275 except the outermost and innermost implications are biconditionals. (Contributed by Alan Sare, 6-Nov-2017.)
Hypothesis
Ref Expression
bi13imp2.1 (𝜑 ↔ (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
bi13imp2 ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem bi13imp2
StepHypRef Expression
1 bi13imp2.1 . . 3 (𝜑 ↔ (𝜓 → (𝜒𝜃)))
21biimpi 206 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32bi33imp12 39013 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  w3a 1054
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  df-3an 1056
This theorem is referenced by: (None)
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