Metamath Proof Explorer


Theorem hlpos

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

Ref Expression
Assertion hlpos ( 𝐾 ∈ HL → 𝐾 ∈ Poset )

Proof

Step Hyp Ref Expression
1 hllat ( 𝐾 ∈ HL → 𝐾 ∈ Lat )
2 latpos ( 𝐾 ∈ Lat → 𝐾 ∈ Poset )
3 1 2 syl ( 𝐾 ∈ HL → 𝐾 ∈ Poset )