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	$$⊢K\in \mathrm{CvLat}\to K\in \mathrm{Poset}$$

Proof

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