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Metamath Proof Explorer

Theorem e03

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e03.1	$⊢ φ$
	e03.2	$⊢ (ψ, χ, θ \to τ)$
	e03.3	$⊢ φ \to (τ \to η)$
Assertion	e03	$⊢ (ψ, χ, θ \to η)$

Proof

Step	Hyp	Ref	Expression
1		e03.1	$⊢ φ$
2		e03.2	$⊢ (ψ, χ, θ \to τ)$
3		e03.3	$⊢ φ \to (τ \to η)$
4	1	vd03	$⊢ (ψ, χ, θ \to φ)$
5	4 2 3	e33	$⊢ (ψ, χ, θ \to η)$