Metamath Proof Explorer


Theorem mpbidi

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 9-Aug-1994)

Ref Expression
Hypotheses mpbidi.min ( 𝜃 → ( 𝜑𝜓 ) )
mpbidi.maj ( 𝜑 → ( 𝜓𝜒 ) )
Assertion mpbidi ( 𝜃 → ( 𝜑𝜒 ) )

Proof

Step Hyp Ref Expression
1 mpbidi.min ( 𝜃 → ( 𝜑𝜓 ) )
2 mpbidi.maj ( 𝜑 → ( 𝜓𝜒 ) )
3 2 biimpd ( 𝜑 → ( 𝜓𝜒 ) )
4 1 3 sylcom ( 𝜃 → ( 𝜑𝜒 ) )