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Metamath Proof Explorer

Theorem e011

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

	Ref	Expression
Hypotheses	e011.1	$⊢ φ$
	e011.2	$⊢ (ψ \to χ)$
	e011.3	$⊢ (ψ \to θ)$
	e011.4	$⊢ φ \to (χ \to (θ \to τ))$
Assertion	e011	$⊢ (ψ \to τ)$

Proof

Step	Hyp	Ref	Expression
1		e011.1	$⊢ φ$
2		e011.2	$⊢ (ψ \to χ)$
3		e011.3	$⊢ (ψ \to θ)$
4		e011.4	$⊢ φ \to (χ \to (θ \to τ))$
5	1	vd01	$⊢ (ψ \to φ)$
6	5 2 3 4	e111	$⊢ (ψ \to τ)$