Metamath Proof Explorer


Theorem bi3impa

Description: Similar to 3impa with implication in hypothesis replaced by biconditional. (Contributed by Alan Sare, 6-Nov-2017)

Ref Expression
Hypothesis bi3impa.1 ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) ↔ 𝜃 )
Assertion bi3impa ( ( 𝜑𝜓𝜒 ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 bi3impa.1 ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) ↔ 𝜃 )
2 1 biimpi ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) → 𝜃 )
3 2 3impa ( ( 𝜑𝜓𝜒 ) → 𝜃 )