 We present the axiomatics. The primitive notions of this theory are equality \((=)\) and the two flavors \(\in\) and \(\varepsilon\) of membership. A formula \(\phi\) is uniform if it does not mention \(\varepsilon\). If \(\phi\) is a uniform formula, \(\phi^*\) is the corresponding formula with \(\in\) replaced by \(\varepsilon\) throughout. A set \(A\) is regular iff it has the same extension with respect to both membership relations: \(x \in A \equiv x \varepsilon A\).