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Theorem bi33imp12 37717
Description: 3imp 1249 with innermost implication of the hypothesis a biconditional. (Contributed by Alan Sare, 6-Nov-2017.)
Hypothesis
Ref Expression
bi33imp12.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
bi33imp12 ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem bi33imp12
StepHypRef Expression
1 bi33imp12.1 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
2 biimp 204 . . 3 ((𝜒𝜃) → (𝜒𝜃))
31, 2syl6 34 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
433imp 1249 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  w3a 1031
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 196  df-an 385  df-3an 1033
This theorem is referenced by:  bi13imp2  37720
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