The expression \neg(x\in x) is a bounded one and thus allowed in separation. By virtue of the rejection of the final disjunct above, \neg sEy, Russel's construction shows that \{x\in y\mid x\notin x\}\notin y. So for any set y, Predicative Separation alone implies that there exists a set which is not a member of y. In particular, no universal set can exist in this theory.
