Theorem sylanbr

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

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

Proof

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