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 )