Theorem sylan2b

Description: A syllogism inference. (Contributed by NM, 21-Apr-1994)

	Ref	Expression
Hypotheses	sylan2b.1	|- ( ph <-> ch )
	sylan2b.2	|- ( ( ps /\ ch ) -> th )
Assertion	sylan2b	|- ( ( ps /\ ph ) -> th )

Proof

Step	Hyp	Ref	Expression
1		sylan2b.1	|- ( ph <-> ch )
2		sylan2b.2	|- ( ( ps /\ ch ) -> th )
3	1	biimpi	|- ( ph -> ch )
4	3 2	sylan2	|- ( ( ps /\ ph ) -> th )