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Metamath Proof Explorer

Theorem hlpos

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

		Ref	Expression
	Assertion	hlpos	$⊢ K \in HL \to K \in Poset$

Step	Hyp	Ref	Expression
1		hllat	$⊢ K \in HL \to K \in Lat$
2		latpos	$⊢ K \in Lat \to K \in Poset$
3	1 2	syl	$⊢ K \in HL \to K \in Poset$