Theorem a2i

Description: Inference distributing an antecedent. Inference associated with ax-2 . Its associated inference is mpd . (Contributed by NM, 29-Dec-1992)

	Ref	Expression
Hypothesis	a2i.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	a2i	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		a2i.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		ax-2	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)$$
3	1 2	ax-mp	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)$$