Is there a finite equational basis for this metric space structure?

Question

Consider the algebraic structure $(\mathbb{R};d,0)$, where $d$ is the distance $|x - y|$ between two real numbers. Is there a finite equational basis for the identities of that structure? I conjecture that the commutative law and the equation $d(x,x)=0$ is sufficient. Is it, and if not, is there a further finite basis, or is there no finite basis?