Actually, I think I'd probably classify just *one* as an axiom - all data must have an unambiguous reference.
The rest of it simply defines what makes a relational (as opposed to any other) database. A bit like Euclid's "parallel lines never meet" defines the *sub*set of geometry that is Euclidean, but does not define geometry itself (and, in defining a subset, defines itself as a constraint not an axiom).