Theorem mp3an

Description: An inference based on modus ponens. (Contributed by NM, 14-May-1999)

	Ref	Expression
Hypotheses	mp3an.1	|- ph
	mp3an.2	|- ps
	mp3an.3	|- ch
	mp3an.4	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	mp3an	|- th

Proof

Step	Hyp	Ref	Expression
1		mp3an.1	|- ph
2		mp3an.2	|- ps
3		mp3an.3	|- ch
4		mp3an.4	|- ( ( ph /\ ps /\ ch ) -> th )
5	1 4	mp3an1	|- ( ( ps /\ ch ) -> th )
6	2 3 5	mp2an	|- th