Theorem imim2i

Description: Inference adding common antecedents in an implication. Inference associated with imim2 . Its associated inference is syl . (Contributed by NM, 28-Dec-1992)

	Ref	Expression
Hypothesis	imim2i.1	$$⊢\phi \to \psi$$
Assertion	imim2i	$$⊢\left(\chi \to \phi \right)\to \left(\chi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		imim2i.1	$$⊢\phi \to \psi$$
2	1	a1i	$$⊢\chi \to \left(\phi \to \psi \right)$$
3	2	a2i	$$⊢\left(\chi \to \phi \right)\to \left(\chi \to \psi \right)$$