Metamath Proof Explorer


Theorem dfvd2impr

Description: A 2-antecedent nested implication implies its virtual deduction form. (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion dfvd2impr ( ( 𝜑 → ( 𝜓𝜒 ) ) → (    𝜑    ,    𝜓    ▶    𝜒    ) )

Proof

Step Hyp Ref Expression
1 dfvd2 ( (    𝜑    ,    𝜓    ▶    𝜒    ) ↔ ( 𝜑 → ( 𝜓𝜒 ) ) )
2 1 biimpri ( ( 𝜑 → ( 𝜓𝜒 ) ) → (    𝜑    ,    𝜓    ▶    𝜒    ) )