Theorem mp3anl1

Description: An inference based on modus ponens. (Contributed by NM, 24-Feb-2005)

	Ref	Expression
Hypotheses	mp3anl1.1	|- ph
	mp3anl1.2	|- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )
Assertion	mp3anl1	|- ( ( ( ps /\ ch ) /\ th ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		mp3anl1.1	|- ph
2		mp3anl1.2	|- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )
3	2	ex	|- ( ( ph /\ ps /\ ch ) -> ( th -> ta ) )
4	1 3	mp3an1	|- ( ( ps /\ ch ) -> ( th -> ta ) )
5	4	imp	|- ( ( ( ps /\ ch ) /\ th ) -> ta )