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Metamath Proof Explorer

Theorem hlclat

Description: A Hilbert lattice is complete. (Contributed by NM, 20-Oct-2011)

		Ref	Expression
	Assertion	hlclat	$⊢ K \in HL \to K \in CLat$

Step	Hyp	Ref	Expression
1		hlomcmcv	$⊢ K \in HL \to (K \in OML \land K \in CLat \land K \in CvLat)$
2	1	simp2d	$⊢ K \in HL \to K \in CLat$