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 ∈ CvLat → 𝐾 ∈ Poset )

Proof

Step	Hyp	Ref	Expression
1		cvllat	⊢ ( 𝐾 ∈ CvLat → 𝐾 ∈ Lat )
2		latpos	⊢ ( 𝐾 ∈ Lat → 𝐾 ∈ Poset )
3	1 2	syl	⊢ ( 𝐾 ∈ CvLat → 𝐾 ∈ Poset )