Theorem mp3an13

Description: An inference based on modus ponens. (Contributed by NM, 14-Jul-2005)

	Ref	Expression
Hypotheses	mp3an13.1	|- ph
	mp3an13.2	|- ch
	mp3an13.3	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	mp3an13	|- ( ps -> th )

Proof

Step	Hyp	Ref	Expression
1		mp3an13.1	|- ph
2		mp3an13.2	|- ch
3		mp3an13.3	|- ( ( ph /\ ps /\ ch ) -> th )
4	2 3	mp3an3	|- ( ( ph /\ ps ) -> th )
5	1 4	mpan	|- ( ps -> th )