This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem cvlposN

Description: An atomic lattice with the covering property is a poset. (Contributed by NM, 5-Nov-2012) (New usage is discouraged.)

		Ref	Expression
	Assertion	cvlposN	$⊢ K \in CvLat \to K \in Poset$

Step	Hyp	Ref	Expression
1		cvllat	$⊢ K \in CvLat \to K \in Lat$
2		latpos	$⊢ K \in Lat \to K \in Poset$
3	1 2	syl	$⊢ K \in CvLat \to K \in Poset$