Metamath Proof Explorer

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	$⊢ ((φ, ψ, χ) \to θ) \leftrightarrow ((φ \land ψ \land χ) \to θ)$

Proof

Step	Hyp	Ref	Expression
1		df-vd1	$⊢ ((φ, ψ, χ) \to θ) \leftrightarrow ((φ, ψ, χ) \to θ)$
2		df-vhc3	$⊢ (φ, ψ, χ) \leftrightarrow (φ \land ψ \land χ)$
3	2	imbi1i	$⊢ ((φ, ψ, χ) \to θ) \leftrightarrow ((φ \land ψ \land χ) \to θ)$
4	1 3	bitri	$⊢ ((φ, ψ, χ) \to θ) \leftrightarrow ((φ \land ψ \land χ) \to θ)$