Theorem sylanr1

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

	Ref	Expression
Hypotheses	sylanr1.1	|- ( ph -> ch )
	sylanr1.2	|- ( ( ps /\ ( ch /\ th ) ) -> ta )
Assertion	sylanr1	|- ( ( ps /\ ( ph /\ th ) ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		sylanr1.1	|- ( ph -> ch )
2		sylanr1.2	|- ( ( ps /\ ( ch /\ th ) ) -> ta )
3	1	anim1i	|- ( ( ph /\ th ) -> ( ch /\ th ) )
4	3 2	sylan2	|- ( ( ps /\ ( ph /\ th ) ) -> ta )