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Metamath Proof Explorer

Theorem hllat

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

		Ref	Expression
	Assertion	hllat	$⊢ K \in HL \to K \in Lat$

Step	Hyp	Ref	Expression
1		hlatl	$⊢ K \in HL \to K \in AtLat$
2		atllat	$⊢ K \in AtLat \to K \in Lat$
3	1 2	syl	$⊢ K \in HL \to K \in Lat$