I don't know if this is exactly what you're looking for, but it's a theorem of NFU that $|\mathcal{P}(V)| < |V|$---which has as a corollary not only that there are atoms, but that the set of atoms is equipollent with the universe.

(A somewhat more disquieting way of putting this is that there are more atoms than there are sets.)

I don't know if this is exactly what you're looking for, but it's a theorem of NFU+Choice that $|\mathcal{P}(V)| < |V|$---which has as a corollary not only that there are atoms, but that the set of atoms is equipollent with the universe.

(A somewhat more disquieting way of putting this is that there are more atoms than there are sets.)