Theorem hllat

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

	Ref	Expression
Assertion	hllat	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ Lat )

Proof

Step	Hyp	Ref	Expression
1		hlatl	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ AtLat )
2		atllat	⊢ ( 𝐾 ∈ AtLat → 𝐾 ∈ Lat )
3	1 2	syl	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ Lat )