Theorem mp3anr1

Description: An inference based on modus ponens. (Contributed by NM, 4-Nov-2006)

	Ref	Expression
Hypotheses	mp3anr1.1	|- ps
	mp3anr1.2	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
Assertion	mp3anr1	|- ( ( ph /\ ( ch /\ th ) ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		mp3anr1.1	|- ps
2		mp3anr1.2	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
3	2	ancoms	|- ( ( ( ps /\ ch /\ th ) /\ ph ) -> ta )
4	1 3	mp3anl1	|- ( ( ( ch /\ th ) /\ ph ) -> ta )
5	4	ancoms	|- ( ( ph /\ ( ch /\ th ) ) -> ta )