Theorem dfvd2an

Description: Definition of a 2-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	dfvd2an	⊢ ( (    (    𝜑    ,    𝜓    )    ▶    𝜒    ) ↔ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		df-vd1	⊢ ( (    (    𝜑    ,    𝜓    )    ▶    𝜒    ) ↔ ( (    𝜑    ,    𝜓    ) → 𝜒 ) )
2		df-vhc2	⊢ ( (    𝜑    ,    𝜓    ) ↔ ( 𝜑 ∧ 𝜓 ) )
3	2	imbi1i	⊢ ( ( (    𝜑    ,    𝜓    ) → 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )
4	1 3	bitri	⊢ ( (    (    𝜑    ,    𝜓    )    ▶    𝜒    ) ↔ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )