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Metamath Proof Explorer

Theorem dfvd2imp

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

Ref Expression
Assertion dfvd2imp ( (    𝜑    ,    𝜓    ▶    𝜒    ) → ( 𝜑 → ( 𝜓 → 𝜒 ) ) )

Proof

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