Theorem hlatl

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

	Ref	Expression
Assertion	hlatl	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ AtLat )

Proof

Step	Hyp	Ref	Expression
1		hlcvl	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ CvLat )
2		cvlatl	⊢ ( 𝐾 ∈ CvLat → 𝐾 ∈ AtLat )
3	1 2	syl	⊢ ( 𝐾 ∈ HL → 𝐾 ∈ AtLat )