Theorem dfvd3an

Description: Definition of a 3-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	dfvd3an	⊢ ( (    (    𝜑    ,    𝜓    ,    𝜒    )    ▶    𝜃    ) ↔ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		df-vd1	⊢ ( (    (    𝜑    ,    𝜓    ,    𝜒    )    ▶    𝜃    ) ↔ ( (    𝜑    ,    𝜓    ,    𝜒    ) → 𝜃 ) )
2		df-vhc3	⊢ ( (    𝜑    ,    𝜓    ,    𝜒    ) ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )
3	2	imbi1i	⊢ ( ( (    𝜑    ,    𝜓    ,    𝜒    ) → 𝜃 ) ↔ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) )
4	1 3	bitri	⊢ ( (    (    𝜑    ,    𝜓    ,    𝜒    )    ▶    𝜃    ) ↔ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) )