Metamath Proof Explorer


Theorem bi33imp12

Description: 3imp with innermost implication of the hypothesis a biconditional. (Contributed by Alan Sare, 6-Nov-2017)

Ref Expression
Hypothesis bi33imp12.1 ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
Assertion bi33imp12 ( ( 𝜑𝜓𝜒 ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 bi33imp12.1 ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
2 biimp ( ( 𝜒𝜃 ) → ( 𝜒𝜃 ) )
3 1 2 syl6 ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
4 3 3imp ( ( 𝜑𝜓𝜒 ) → 𝜃 )