Theorem mp3an12

Description: An inference based on modus ponens. (Contributed by NM, 13-Jul-2005)

	Ref	Expression
Hypotheses	mp3an12.1	|- ph
	mp3an12.2	|- ps
	mp3an12.3	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	mp3an12	|- ( ch -> th )

Proof

Step	Hyp	Ref	Expression
1		mp3an12.1	|- ph
2		mp3an12.2	|- ps
3		mp3an12.3	|- ( ( ph /\ ps /\ ch ) -> th )
4	1 3	mp3an1	|- ( ( ps /\ ch ) -> th )
5	2 4	mpan	|- ( ch -> th )