We give a first order formulation of Church's type theory in which types are mere sets. This formulation is obtained by replacing $\lambda$-calculus by a language of combinators (skolemized comprehension scheme), introducing a distinction between propositions and their contents, relativizing quantifiers and at last replacing typing predicates by membership to some sets. The theory obtained this way has both a type theoretical flavor and a set theoretical one. Like set theory, it is a first order theory, and it uses only one notion of collection. Like type theory, it gives an explicit notation for objects, a primitive notion of function and propositions are objects.