Metamath Proof Explorer


Theorem bi123impib

Description: 3impib with the implications of the hypothesis biconditionals. (Contributed by Alan Sare, 6-Nov-2017)

Ref Expression
Hypothesis bi123impib.1 ( 𝜑 ↔ ( ( 𝜓𝜒 ) ↔ 𝜃 ) )
Assertion bi123impib ( ( 𝜑𝜓𝜒 ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 bi123impib.1 ( 𝜑 ↔ ( ( 𝜓𝜒 ) ↔ 𝜃 ) )
2 1 biimpi ( 𝜑 → ( ( 𝜓𝜒 ) ↔ 𝜃 ) )
3 2 bi23impib ( ( 𝜑𝜓𝜒 ) → 𝜃 )