The notion of double Boolean algebra was introduced by Wille to explore the equational class of protoconcept algebras. Many authors have studied fundamental results, including the Prime Ideal Theorem, topological representation, and the congruence structure for dBas. Double Boolean algebras are defined by a set of 23 equations given in the subsequent definition. Definition: An algebra 𝕯 := (D, ⊔, ⊓, ¬, ⌟, ⊤, ⊥) satisfying the following properties is called a double Boolean algebra (dBa). For any 𝑥, 𝑦, 𝑧 ∈ D we require (1a)(𝑥 ⊓ 𝑥) ⊓ 𝑦 = 𝑥 ⊓ 𝑦 (1b)(𝑥 ⊔ 𝑥) ⊔ 𝑦 = 𝑥 ⊔ 𝑦 (2a)𝑥 ⊓ 𝑦 = 𝑦 ⊓ 𝑥 (2b)𝑥 ⊔ 𝑦 = 𝑦 ⊔ 𝑥 (3a)¬(𝑥 ⊓ 𝑥) = ¬𝑥 (3b)⌟(𝑥 ⊔ 𝑥) = ⌟𝑥 (4a)𝑥 ⊓ (𝑥 ⊔ 𝑦) = 𝑥 ⊓ 𝑥 (4b)𝑥 ⊔ (𝑥 ⊓ 𝑦) = 𝑥 ⊔ 𝑥 (5a)𝑥 ⊓ (𝑦 ∨ 𝑧) = (𝑥 ⊓ 𝑦) ∨ (𝑥 ⊓ 𝑧) (5b)𝑥 ⊔ (𝑦 ∧ 𝑧) = (𝑥 ⊔ 𝑦) ∧ (𝑥 ⊔ 𝑧) (6a)𝑥 ⊓ (𝑥 ∨ 𝑦) = 𝑥 ⊓ 𝑥 (6b)𝑥 ⊔ (𝑥 ∧ 𝑦) = 𝑥 ⊔ 𝑥 (7a)¬¬(𝑥 ⊓ 𝑦) = 𝑥 ⊓ 𝑦 (7b)⌟⌟(𝑥 ⊔ 𝑦) = 𝑥 ⊔ 𝑦 (8a)𝑥 ⊓ ¬𝑥 = ⊥ (8b)𝑥 ⊔ ⌟𝑥 = ⊤ (9a)¬⊤ = ⊥ (9b)⌟⊥ = ⊤ (10a)𝑥 ⊓ (𝑦 ⊓ 𝑧) = (𝑥 ⊓ 𝑦) ⊓ 𝑧 (10b)𝑥 ⊔ (𝑦 ⊔ 𝑧) = (𝑥 ⊔ 𝑦) ⊔ 𝑧 (11a)¬⊥ = ⊤ ⊓ ⊤ (11b)⌟⊤ = ⊥ ⊔ ⊥ (12)(𝑥 ⊓ 𝑥) ⊔ (𝑥 ⊓ 𝑥) = (𝑥 ⊔ 𝑥) ⊓ (𝑥 ⊔ 𝑥) where 𝑥 ∨ 𝑦 ≔ ¬(¬𝑥 ⊓ ¬𝑦) and 𝑥 ∧ 𝑦 ≔ ⌟(⌟𝑥 ⊔ ⌟𝑦). This is a relatively long list, which might refrain potential users to engage in investigating or applying these structures. In previous work, it was shown that the axioms (1a), (1b) and (11a), (11b) can be derived from other axioms of dBa. During a conference in Cádiz, the authors identified a shared interest in simplifying the axiomatization of dBas. As a result, we collaborated on developing a more streamlined, redundancy-free axiomatization. Let DAxom be the set of all axioms of dBa and MCore be the subset of DAxom consisting of the axioms 2a, 2b, 3a, 3b, 4a, 4b, 5a, 5b 8a, 8b and 12. Then we have the following result: Theorem: There is a six-element non-dBa 𝕯 such that 𝕯 satisfies all the equations in MCore but does not satisfy the axioms 7a and 7b. The above theorem suggests that we need MCore and the axioms 7a and 7b to define a dBa. We denote DCore := MCore ∪ {¬¬(x ⊓ y) = x ⊓ y, ⌟⌟(x ⊔ y) = x ⊔ y}. Theorem: An algebra (D, ⊔, ⊓, ¬, ⌟, ⊤, ⊥) is a dBa if and only if it satisfies DCore. Moreover DCore is a minimal set of axioms for such an algebra.