Theorem mpan2

Description: An inference based on modus ponens. (Contributed by NM, 16-Sep-1993) (Proof shortened by Wolf Lammen, 19-Nov-2012)

	Ref	Expression
Hypotheses	mpan2.1	|- ps
	mpan2.2	|- ( ( ph /\ ps ) -> ch )
Assertion	mpan2	|- ( ph -> ch )

Proof

Step	Hyp	Ref	Expression
1		mpan2.1	|- ps
2		mpan2.2	|- ( ( ph /\ ps ) -> ch )
3	1	a1i	|- ( ph -> ps )
4	3 2	mpdan	|- ( ph -> ch )