Metamath Proof Explorer

Theorem hlcvl

Description: A Hilbert lattice is an atomic lattice with the covering property. (Contributed by NM, 5-Nov-2012)

Ref Expression
Assertion hlcvl 
|- ( K e. HL -> K e. CvLat )

Proof

Step Hyp Ref Expression
1 hlomcmcv 
 |-  ( K e. HL -> ( K e. OML /\ K e. CLat /\ K e. CvLat ) )
2 1 simp3d 
 |-  ( K e. HL -> K e. CvLat )