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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 ∈ OL → 𝐾 ∈ Lat )

Proof

Step Hyp Ref Expression
1 isolat ⊢ ( 𝐾 ∈ OL ↔ ( 𝐾 ∈ Lat ∧ 𝐾 ∈ OP ) )
2 1 simplbi ⊢ ( 𝐾 ∈ OL → 𝐾 ∈ Lat )