Theorem imim12i

Description: Inference joining two implications. Inference associated with imim12 . Its associated inference is 3syl . (Contributed by NM, 12-Mar-1993) (Proof shortened by Mel L. O'Cat, 29-Oct-2011)

	Ref	Expression
Hypotheses	imim12i.1	$$⊢\phi \to \psi$$
	imim12i.2	$$⊢\chi \to \theta$$
Assertion	imim12i	$$⊢\left(\psi \to \chi \right)\to \left(\phi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		imim12i.1	$$⊢\phi \to \psi$$
2		imim12i.2	$$⊢\chi \to \theta$$
3	2	imim2i	$$⊢\left(\psi \to \chi \right)\to \left(\psi \to \theta \right)$$
4	1 3	syl5	$$⊢\left(\psi \to \chi \right)\to \left(\phi \to \theta \right)$$