Let's consider the "axiom 0" of ZFC: $\exists x (x=x)$
I "think to" it as "there exist something which is equal to itself, in other words there exist at least something".
But on the notes where I am studying I find: "There exists at least a set".
My question is: what is the correct interpretation? If the latter, why $x$ must be a set and can't be a proper class, for example?
Thanks in advance.