Theorem imim3i

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

	Ref	Expression
Hypothesis	imim3i.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	imim3i	$$⊢\left(\theta \to \phi \right)\to \left(\left(\theta \to \psi \right)\to \left(\theta \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		imim3i.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2	1	imim2i	$$⊢\left(\theta \to \phi \right)\to \left(\theta \to \left(\psi \to \chi \right)\right)$$
3	2	a2d	$$⊢\left(\theta \to \phi \right)\to \left(\left(\theta \to \psi \right)\to \left(\theta \to \chi \right)\right)$$