Theorem hlop

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

	Ref	Expression
Assertion	hlop	$$⊢K\in \mathrm{HL}\to K\in \mathrm{OP}$$

Proof

Step	Hyp	Ref	Expression
1		hlol	$$⊢K\in \mathrm{HL}\to K\in \mathrm{OL}$$
2		olop	$$⊢K\in \mathrm{OL}\to K\in \mathrm{OP}$$
3	1 2	syl	$$⊢K\in \mathrm{HL}\to K\in \mathrm{OP}$$