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Metamath Proof Explorer

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 ) )