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Metamath Proof Explorer

Theorem e211

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e211.1	$⊢ (φ, ψ \to χ)$
	e211.2	$⊢ (φ \to θ)$
	e211.3	$⊢ (φ \to τ)$
	e211.4	$⊢ χ \to (θ \to (τ \to η))$
Assertion	e211	$⊢ (φ, ψ \to η)$

Proof

Step	Hyp	Ref	Expression
1		e211.1	$⊢ (φ, ψ \to χ)$
2		e211.2	$⊢ (φ \to θ)$
3		e211.3	$⊢ (φ \to τ)$
4		e211.4	$⊢ χ \to (θ \to (τ \to η))$
5	2	vd12	$⊢ (φ, ψ \to θ)$
6	3	vd12	$⊢ (φ, ψ \to τ)$
7	1 5 6 4	e222	$⊢ (φ, ψ \to η)$