Theorem ollat

Description: An ortholattice is a lattice. (Contributed by NM, 18-Sep-2011)

	Ref	Expression
Assertion	ollat	⊢ ( 𝐾 ∈ OL → 𝐾 ∈ Lat )

Proof

Step	Hyp	Ref	Expression
1		isolat	⊢ ( 𝐾 ∈ OL ↔ ( 𝐾 ∈ Lat ∧ 𝐾 ∈ OP ) )
2	1	simplbi	⊢ ( 𝐾 ∈ OL → 𝐾 ∈ Lat )