Theorem mp3an3

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

	Ref	Expression
Hypotheses	mp3an3.1	|- ch
	mp3an3.2	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	mp3an3	|- ( ( ph /\ ps ) -> th )

Proof

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