Theorem sylanbrc

Description: Syllogism inference. (Contributed by Jeff Madsen, 2-Sep-2009)

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

Proof

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