Metamath Proof Explorer

Theorem hlclat

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

Ref Expression
Assertion hlclat ⊢ K ∈ HL → K ∈ CLat

Proof

Step Hyp Ref Expression
1 hlomcmcv ⊢ K ∈ HL → K ∈ OML ∧ K ∈ CLat ∧ K ∈ CvLat
2 1 simp2d ⊢ K ∈ HL → K ∈ CLat