Theorem hlatl

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

	Ref	Expression
Assertion	hlatl	$$⊢K\in \mathrm{HL}\to K\in \mathrm{AtLat}$$

Proof

Step	Hyp	Ref	Expression
1		hlcvl	$$⊢K\in \mathrm{HL}\to K\in \mathrm{CvLat}$$
2		cvlatl	$$⊢K\in \mathrm{CvLat}\to K\in \mathrm{AtLat}$$
3	1 2	syl	$$⊢K\in \mathrm{HL}\to K\in \mathrm{AtLat}$$