Metamath Proof Explorer

Theorem e323

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 17-Apr-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e323.1	$⊢ (φ, ψ, χ \to θ)$
	e323.2	$⊢ (φ, ψ \to τ)$
	e323.3	$⊢ (φ, ψ, χ \to η)$
	e323.4	$⊢ θ \to (τ \to (η \to ζ))$
Assertion	e323	$⊢ (φ, ψ, χ \to ζ)$

Proof

Step	Hyp	Ref	Expression
1		e323.1	$⊢ (φ, ψ, χ \to θ)$
2		e323.2	$⊢ (φ, ψ \to τ)$
3		e323.3	$⊢ (φ, ψ, χ \to η)$
4		e323.4	$⊢ θ \to (τ \to (η \to ζ))$
5	1	dfvd3i	$⊢ φ \to (ψ \to (χ \to θ))$
6	2	dfvd2i	$⊢ φ \to (ψ \to τ)$
7	3	dfvd3i	$⊢ φ \to (ψ \to (χ \to η))$
8	5 6 7 4	ee323	$⊢ φ \to (ψ \to (χ \to ζ))$
9	8	dfvd3ir	$⊢ (φ, ψ, χ \to ζ)$