Theorem hlpos

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

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

Proof

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