Theorem isolat

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

	Ref	Expression
Assertion	isolat	⊢ ( 𝐾 ∈ OL ↔ ( 𝐾 ∈ Lat ∧ 𝐾 ∈ OP ) )

Proof

Step	Hyp	Ref	Expression
1		df-ol	⊢ OL = ( Lat ∩ OP )
2	1	elin2	⊢ ( 𝐾 ∈ OL ↔ ( 𝐾 ∈ Lat ∧ 𝐾 ∈ OP ) )