Theorem imim1i

Description: Inference adding common consequents in an implication, thereby interchanging the original antecedent and consequent. Inference associated with imim1 . Its associated inference is syl . (Contributed by NM, 28-Dec-1992) (Proof shortened by Wolf Lammen, 4-Aug-2012)

	Ref	Expression
Hypothesis	imim1i.1	$$⊢\phi \to \psi$$
Assertion	imim1i	$$⊢\left(\psi \to \chi \right)\to \left(\phi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		imim1i.1	$$⊢\phi \to \psi$$
2		id	$$⊢\chi \to \chi$$
3	1 2	imim12i	$$⊢\left(\psi \to \chi \right)\to \left(\phi \to \chi \right)$$