Theorem sylanl1

Description: A syllogism inference. (Contributed by NM, 10-Mar-2005)

	Ref	Expression
Hypotheses	sylanl1.1	|- ( ph -> ps )
	sylanl1.2	|- ( ( ( ps /\ ch ) /\ th ) -> ta )
Assertion	sylanl1	|- ( ( ( ph /\ ch ) /\ th ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		sylanl1.1	|- ( ph -> ps )
2		sylanl1.2	|- ( ( ( ps /\ ch ) /\ th ) -> ta )
3	1	anim1i	|- ( ( ph /\ ch ) -> ( ps /\ ch ) )
4	3 2	sylan	|- ( ( ( ph /\ ch ) /\ th ) -> ta )