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Metamath Proof Explorer

Theorem ollat

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

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

Step	Hyp	Ref	Expression
1		isolat	$⊢ K \in OL \leftrightarrow (K \in Lat \land K \in OP)$
2	1	simplbi	$⊢ K \in OL \to K \in Lat$