Metamath Proof Explorer

Theorem hloml

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

Ref Expression
Assertion hloml 
|- ( K e. HL -> K e. OML )

Proof

Step Hyp Ref Expression
1 hlomcmcv 
 |-  ( K e. HL -> ( K e. OML /\ K e. CLat /\ K e. CvLat ) )
2 1 simp1d 
 |-  ( K e. HL -> K e. OML )