Theorem mp3an1

Description: An inference based on modus ponens. (Contributed by NM, 21-Nov-1994)

	Ref	Expression
Hypotheses	mp3an1.1	|- ph
	mp3an1.2	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	mp3an1	|- ( ( ps /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		mp3an1.1	|- ph
2		mp3an1.2	|- ( ( ph /\ ps /\ ch ) -> th )
3	2	3expb	|- ( ( ph /\ ( ps /\ ch ) ) -> th )
4	1 3	mpan	|- ( ( ps /\ ch ) -> th )