Theorem hllat

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

	Ref	Expression
Assertion	hllat	$$⊢K\in \mathrm{HL}\to K\in \mathrm{Lat}$$

Proof

Step	Hyp	Ref	Expression
1		hlatl	$$⊢K\in \mathrm{HL}\to K\in \mathrm{AtLat}$$
2		atllat	$$⊢K\in \mathrm{AtLat}\to K\in \mathrm{Lat}$$
3	1 2	syl	$$⊢K\in \mathrm{HL}\to K\in \mathrm{Lat}$$