Theorem mp3an2

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

	Ref	Expression
Hypotheses	mp3an2.1	|- ps
	mp3an2.2	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	mp3an2	|- ( ( ph /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		mp3an2.1	|- ps
2		mp3an2.2	|- ( ( ph /\ ps /\ ch ) -> th )
3	2	3expa	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
4	1 3	mpanl2	|- ( ( ph /\ ch ) -> th )