Theorem ollat

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

	Ref	Expression
Assertion	ollat	$$⊢K\in \mathrm{OL}\to K\in \mathrm{Lat}$$

Proof

Step	Hyp	Ref	Expression
1		isolat	$$⊢K\in \mathrm{OL}\leftrightarrow \left(K\in \mathrm{Lat}\wedge K\in \mathrm{OP}\right)$$
2	1	simplbi	$$⊢K\in \mathrm{OL}\to K\in \mathrm{Lat}$$