Theorem hlol

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

	Ref	Expression
Assertion	hlol	$$⊢K\in \mathrm{HL}\to K\in \mathrm{OL}$$

Proof

Step	Hyp	Ref	Expression
1		hloml	$$⊢K\in \mathrm{HL}\to K\in \mathrm{OML}$$
2		omlol	$$⊢K\in \mathrm{OML}\to K\in \mathrm{OL}$$
3	1 2	syl	$$⊢K\in \mathrm{HL}\to K\in \mathrm{OL}$$