Theorem syl3an3br

Description: A syllogism inference. (Contributed by NM, 22-Aug-1995)

	Ref	Expression
Hypotheses	syl3an3br.1	|- ( th <-> ph )
	syl3an3br.2	|- ( ( ps /\ ch /\ th ) -> ta )
Assertion	syl3an3br	|- ( ( ps /\ ch /\ ph ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		syl3an3br.1	|- ( th <-> ph )
2		syl3an3br.2	|- ( ( ps /\ ch /\ th ) -> ta )
3	1	biimpri	|- ( ph -> th )
4	3 2	syl3an3	|- ( ( ps /\ ch /\ ph ) -> ta )