Theorem sylanb

Description: A syllogism inference. (Contributed by NM, 18-May-1994)

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

Proof

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