Theorem hlclat

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

	Ref	Expression
Assertion	hlclat	$$⊢K\in \mathrm{HL}\to K\in \mathrm{CLat}$$

Proof

Step	Hyp	Ref	Expression
1		hlomcmcv	$$⊢K\in \mathrm{HL}\to \left(K\in \mathrm{OML}\wedge K\in \mathrm{CLat}\wedge K\in \mathrm{CvLat}\right)$$
2	1	simp2d	$$⊢K\in \mathrm{HL}\to K\in \mathrm{CLat}$$