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Theorem bi123impia 39012
Description: 3impia 1280 with the implications of the hypothesis biconditionals. (Contributed by Alan Sare, 6-Nov-2017.)
Hypothesis
Ref Expression
bi123impia.1 ((𝜑𝜓) ↔ (𝜒𝜃))
Assertion
Ref Expression
bi123impia ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem bi123impia
StepHypRef Expression
1 bi123impia.1 . . 3 ((𝜑𝜓) ↔ (𝜒𝜃))
21biimpi 206 . 2 ((𝜑𝜓) → (𝜒𝜃))
32biimp3a 1472 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 383  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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