Theorem isolat

Description: The predicate "is an ortholattice." (Contributed by NM, 18-Sep-2011)

	Ref	Expression
Assertion	isolat	$$⊢K\in \mathrm{OL}\leftrightarrow \left(K\in \mathrm{Lat}\wedge K\in \mathrm{OP}\right)$$

Proof

Step	Hyp	Ref	Expression
1		df-ol	$$⊢\mathrm{OL}=\mathrm{Lat}\cap \mathrm{OP}$$
2	1	elin2	$$⊢K\in \mathrm{OL}\leftrightarrow \left(K\in \mathrm{Lat}\wedge K\in \mathrm{OP}\right)$$