Theorem mp3anr3

Description: An inference based on modus ponens. (Contributed by NM, 19-Oct-2007)

	Ref	Expression
Hypotheses	mp3anr3.1	|- th
	mp3anr3.2	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
Assertion	mp3anr3	|- ( ( ph /\ ( ps /\ ch ) ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		mp3anr3.1	|- th
2		mp3anr3.2	|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
3	2	ancoms	|- ( ( ( ps /\ ch /\ th ) /\ ph ) -> ta )
4	1 3	mp3anl3	|- ( ( ( ps /\ ch ) /\ ph ) -> ta )
5	4	ancoms	|- ( ( ph /\ ( ps /\ ch ) ) -> ta )