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 → ( 𝜓 → 𝜒 ) ) → (    𝜑    ,    𝜓    ▶    𝜒    ) )

Proof

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