Theorem hlop

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

	Ref	Expression
Assertion	hlop	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ OP )

Proof

Step	Hyp	Ref	Expression
1		hlol	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ OL )
2		olop	⊢ ( 𝐾 ∈ OL → 𝐾 ∈ OP )
3	1 2	syl	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ OP )