Theorem cvllat

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

	Ref	Expression
Assertion	cvllat	⊢ ( 𝐾 ∈ CvLat → 𝐾 ∈ Lat )

Proof

Step	Hyp	Ref	Expression
1		cvlatl	⊢ ( 𝐾 ∈ CvLat → 𝐾 ∈ AtLat )
2		atllat	⊢ ( 𝐾 ∈ AtLat → 𝐾 ∈ Lat )
3	1 2	syl	⊢ ( 𝐾 ∈ CvLat → 𝐾 ∈ Lat )