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Theorem bi123impib 40698
Description: 3impib 1108 with the implications of the hypothesis biconditionals. (Contributed by Alan Sare, 6-Nov-2017.)
Hypothesis
Ref Expression
bi123impib.1 (𝜑 ↔ ((𝜓𝜒) ↔ 𝜃))
Assertion
Ref Expression
bi123impib ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem bi123impib
StepHypRef Expression
1 bi123impib.1 . . 3 (𝜑 ↔ ((𝜓𝜒) ↔ 𝜃))
21biimpi 217 . 2 (𝜑 → ((𝜓𝜒) ↔ 𝜃))
32bi23impib 40696 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wa 396  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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