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 ∈ 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 )