Metamath Proof Explorer

Theorem hloml

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

Ref Expression
Assertion hloml ⊢ K ∈ HL → K ∈ OML

Proof

Step Hyp Ref Expression
1 hlomcmcv ⊢ K ∈ HL → K ∈ OML ∧ K ∈ CLat ∧ K ∈ CvLat
2 1 simp1d ⊢ K ∈ HL → K ∈ OML