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Metamath Proof Explorer

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 )