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 )