This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

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	$⊢ K \in HL \to K \in CvLat$

Step	Hyp	Ref	Expression
1		hlomcmcv	$⊢ K \in HL \to (K \in OML \land K \in CLat \land K \in CvLat)$
2	1	simp3d	$⊢ K \in HL \to K \in CvLat$