So this is a theorem  from A Shorter Model Theory and I'm being unable to prove this when it seems like proving this would be quite intuitive and straightforward. Does anyone know a proof?
Let L be the empty signature and A an L-structure so that A is simply a set. Let X be any subset of A, and Y be a subset of dom(A) which is definable in A by a formula of some logic of signature L, using parameters from X. Then Y is either a subset of X, or the complement in dom(A) of a subset of X.
 Theorem 2.1.2, page 27.