Theorem isolatiN

Description: Properties that determine an ortholattice. (Contributed by NM, 18-Sep-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	isolati.1	$$⊢K\in \mathrm{Lat}$$
	isolati.2	$$⊢K\in \mathrm{OP}$$
Assertion	isolatiN	$$⊢K\in \mathrm{OL}$$

Proof

Step	Hyp	Ref	Expression
1		isolati.1	$$⊢K\in \mathrm{Lat}$$
2		isolati.2	$$⊢K\in \mathrm{OP}$$
3		isolat	$$⊢K\in \mathrm{OL}\leftrightarrow \left(K\in \mathrm{Lat}\wedge K\in \mathrm{OP}\right)$$
4	1 2 3	mpbir2an	$$⊢K\in \mathrm{OL}$$