Huntington axiom and 0

Question

The Huntington axiom plus associativity and commutativity is equivallent to the Boolean algebra axioms. But the Boolean algebra axioms include properties of the universal bounds 0 and 1. These constants are not mentioned in the Huntington axiom nor in associativity and commutativity laws. How can these properties, such as $\forall x~0 \land x=0$, be proven from the huntington axiom and the associativity and commutativity laws alone, if neither of the two bounds is mentioned in them? (The second bound can be defined using negation from the first, but shouldn't at least one bound be included in a set of axioms for Boolean algebra?).