Theorem dfvd2

Description: Definition of a 2-hypothesis virtual deduction. (Contributed by Alan Sare, 14-Nov-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	dfvd2	⊢ ( (    𝜑    ,    𝜓    ▶    𝜒    ) ↔ ( 𝜑 → ( 𝜓 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		df-vd2	⊢ ( (    𝜑    ,    𝜓    ▶    𝜒    ) ↔ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )
2		impexp	⊢ ( ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ↔ ( 𝜑 → ( 𝜓 → 𝜒 ) ) )
3	1 2	bitri	⊢ ( (    𝜑    ,    𝜓    ▶    𝜒    ) ↔ ( 𝜑 → ( 𝜓 → 𝜒 ) ) )