Definition:Boolean Lattice/Definition 2

Definition
An ordered structure $\left({S, \vee, \wedge, \preceq}\right)$ is a Boolean lattice :

$(1): \quad \left({S, \vee, \wedge}\right)$ is a Boolean algebra

$(2): \quad$ For all $a, b \in S$: $a \wedge b \preceq a \vee b$

Also see

 * Equivalence of Definitions of Boolean Lattice