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Metamath Proof Explorer

Theorem hlatl

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

		Ref	Expression
	Assertion	hlatl	$⊢ K \in HL \to K \in AtLat$

Step	Hyp	Ref	Expression
1		hlcvl	$⊢ K \in HL \to K \in CvLat$
2		cvlatl	$⊢ K \in CvLat \to K \in AtLat$
3	1 2	syl	$⊢ K \in HL \to K \in AtLat$