Theorem hlcvl

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

	Ref	Expression
Assertion	hlcvl	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ CvLat )

Proof

Step	Hyp	Ref	Expression
1		hlomcmcv	⊢ ( 𝐾 ∈ HL → ( 𝐾 ∈ OML ∧ 𝐾 ∈ CLat ∧ 𝐾 ∈ CvLat ) )
2	1	simp3d	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ CvLat )