Theorem hlol

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

	Ref	Expression
Assertion	hlol	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ OL )

Proof

Step	Hyp	Ref	Expression
1		hloml	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ OML )
2		omlol	⊢ ( 𝐾 ∈ OML → 𝐾 ∈ OL )
3	1 2	syl	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ OL )