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Metamath Proof Explorer

Theorem hlclat

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

Ref Expression
Assertion hlclat 
|- ( K e. HL -> K e. CLat )

Proof

Step Hyp Ref Expression
1 hlomcmcv 
 |-  ( K e. HL -> ( K e. OML /\ K e. CLat /\ K e. CvLat ) )
2 1 simp2d 
 |-  ( K e. HL -> K e. CLat )