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 ) ) )