Theorem mpan

Description: An inference based on modus ponens. (Contributed by NM, 30-Aug-1993) (Proof shortened by Wolf Lammen, 7-Apr-2013)

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

Proof

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