Theorem syl3an2br

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

	Ref	Expression
Hypotheses	syl3an2br.1	|- ( ch <-> ph )
	syl3an2br.2	|- ( ( ps /\ ch /\ th ) -> ta )
Assertion	syl3an2br	|- ( ( ps /\ ph /\ th ) -> ta )

Proof

Step	Hyp	Ref	Expression
1		syl3an2br.1	|- ( ch <-> ph )
2		syl3an2br.2	|- ( ( ps /\ ch /\ th ) -> ta )
3	1	biimpri	|- ( ph -> ch )
4	3 2	syl3an2	|- ( ( ps /\ ph /\ th ) -> ta )