Theorem imim3i

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

	Ref	Expression
Hypothesis	imim3i.1	|- ( ph -> ( ps -> ch ) )
Assertion	imim3i	|- ( ( th -> ph ) -> ( ( th -> ps ) -> ( th -> ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		imim3i.1	|- ( ph -> ( ps -> ch ) )
2	1	imim2i	|- ( ( th -> ph ) -> ( th -> ( ps -> ch ) ) )
3	2	a2d	|- ( ( th -> ph ) -> ( ( th -> ps ) -> ( th -> ch ) ) )