Theorem mp3an23

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

	Ref	Expression
Hypotheses	mp3an23.1	|- ps
	mp3an23.2	|- ch
	mp3an23.3	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	mp3an23	|- ( ph -> th )

Proof

Step	Hyp	Ref	Expression
1		mp3an23.1	|- ps
2		mp3an23.2	|- ch
3		mp3an23.3	|- ( ( ph /\ ps /\ ch ) -> th )
4	2 3	mp3an3	|- ( ( ph /\ ps ) -> th )
5	1 4	mpan2	|- ( ph -> th )