  We show that if (M,E,E') satisfies the first order Zermelo-Fraenkel axioms of
set theory when the membership relation is E and also when the membership
relation is E', and in both cases the formulas are allowed to contain both E
and E', then (M,E) and (M,E') are isomorphic, and the isomorphism is definable
in (M,E,E'). This extends Zermelo's 1930 theorem about second order ZFC.
