Theorem sylan

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

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

Proof

Step	Hyp	Ref	Expression
1		sylan.1	|- ( ph -> ps )
2		sylan.2	|- ( ( ps /\ ch ) -> th )
3	2	expcom	|- ( ch -> ( ps -> th ) )
4	1 3	mpan9	|- ( ( ph /\ ch ) -> th )