Theorem sylan2

Description: A syllogism inference. (Contributed by NM, 21-Apr-1994) (Proof shortened by Wolf Lammen, 22-Nov-2012)

	Ref	Expression
Hypotheses	sylan2.1	|- ( ph -> ch )
	sylan2.2	|- ( ( ps /\ ch ) -> th )
Assertion	sylan2	|- ( ( ps /\ ph ) -> th )

Proof

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