Theorem sylanl2

Description: A syllogism inference. (Contributed by NM, 1-Jan-2005)

	Ref	Expression
Hypotheses	sylanl2.1	|- ( ph -> ch )
	sylanl2.2	|- ( ( ( ps /\ ch ) /\ th ) -> ta )
Assertion	sylanl2	|- ( ( ( ps /\ ph ) /\ th ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		sylanl2.1	|- ( ph -> ch )
2		sylanl2.2	|- ( ( ( ps /\ ch ) /\ th ) -> ta )
3	1	adantl	|- ( ( ps /\ ph ) -> ch )
4	3 2	syldanl	|- ( ( ( ps /\ ph ) /\ th ) -> ta )