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 )