Metamath Proof Explorer


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 )