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Metamath Proof Explorer

Theorem e210

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

	Ref	Expression
Hypotheses	e210.1	$⊢ (φ, ψ \to χ)$
	e210.2	$⊢ (φ \to θ)$
	e210.3	$⊢ τ$
	e210.4	$⊢ χ \to (θ \to (τ \to η))$
Assertion	e210	$⊢ (φ, ψ \to η)$

Proof

Step	Hyp	Ref	Expression
1		e210.1	$⊢ (φ, ψ \to χ)$
2		e210.2	$⊢ (φ \to θ)$
3		e210.3	$⊢ τ$
4		e210.4	$⊢ χ \to (θ \to (τ \to η))$
5	3	vd01	$⊢ (φ \to τ)$
6	1 2 5 4	e211	$⊢ (φ, ψ \to η)$