Theorem sylanr2

Description: A syllogism inference. (Contributed by NM, 9-Apr-2005)

	Ref	Expression
Hypotheses	sylanr2.1	|- ( ph -> th )
	sylanr2.2	|- ( ( ps /\ ( ch /\ th ) ) -> ta )
Assertion	sylanr2	|- ( ( ps /\ ( ch /\ ph ) ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		sylanr2.1	|- ( ph -> th )
2		sylanr2.2	|- ( ( ps /\ ( ch /\ th ) ) -> ta )
3	1	anim2i	|- ( ( ch /\ ph ) -> ( ch /\ th ) )
4	3 2	sylan2	|- ( ( ps /\ ( ch /\ ph ) ) -> ta )