Theorem mp3anr2

Description: An inference based on modus ponens. (Contributed by NM, 24-Nov-2006)

	Ref	Expression
Hypotheses	mp3anr2.1	|- ch
	mp3anr2.2	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
Assertion	mp3anr2	|- ( ( ph /\ ( ps /\ th ) ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		mp3anr2.1	|- ch
2		mp3anr2.2	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
3	2	ancoms	|- ( ( ( ps /\ ch /\ th ) /\ ph ) -> ta )
4	1 3	mp3anl2	|- ( ( ( ps /\ th ) /\ ph ) -> ta )
5	4	ancoms	|- ( ( ph /\ ( ps /\ th ) ) -> ta )