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Metamath Proof Explorer

Theorem imim3i

Description: Inference adding three nested antecedents. (Contributed by NM, 19-Dec-2006)

		Ref	Expression
	Hypothesis	imim3i.1	$⊢ φ \to (ψ \to χ)$
	Assertion	imim3i	$⊢ (θ \to φ) \to ((θ \to ψ) \to (θ \to χ))$

Step	Hyp	Ref	Expression
1		imim3i.1	$⊢ φ \to (ψ \to χ)$
2	1	imim2i	$⊢ (θ \to φ) \to (θ \to (ψ \to χ))$
3	2	a2d	$⊢ (θ \to φ) \to ((θ \to ψ) \to (θ \to χ))$