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Theorem bi12imp3 40705
Description: Similar to 3imp 1103 except all but innermost implication are biconditionals. (Contributed by Alan Sare, 6-Nov-2017.)
Hypothesis
Ref Expression
bi12imp3.1 (𝜑 ↔ (𝜓 ↔ (𝜒𝜃)))
Assertion
Ref Expression
bi12imp3 ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem bi12imp3
StepHypRef Expression
1 bi12imp3.1 . . 3 (𝜑 ↔ (𝜓 ↔ (𝜒𝜃)))
21biimpi 217 . 2 (𝜑 → (𝜓 ↔ (𝜒𝜃)))
32bi23imp13 40702 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by: (None)
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