Theorem syl3anbrc

Description: Syllogism inference. (Contributed by Mario Carneiro, 11-May-2014)

	Ref	Expression
Hypotheses	syl3anbrc.1	|- ( ph -> ps )
	syl3anbrc.2	|- ( ph -> ch )
	syl3anbrc.3	|- ( ph -> th )
	syl3anbrc.4	|- ( ta <-> ( ps /\ ch /\ th ) )
Assertion	syl3anbrc	|- ( ph -> ta )

Proof

Step	Hyp	Ref	Expression
1		syl3anbrc.1	|- ( ph -> ps )
2		syl3anbrc.2	|- ( ph -> ch )
3		syl3anbrc.3	|- ( ph -> th )
4		syl3anbrc.4	|- ( ta <-> ( ps /\ ch /\ th ) )
5	1 2 3	3jca	|- ( ph -> ( ps /\ ch /\ th ) )
6	5 4	sylibr	|- ( ph -> ta )