Proving the existence of equilibrium having specified properties is often synonymous with proving the result in trade theory. The Grandmont-McFadden proposition that any autarkic allocation can be replaced by a Pareto superior free trade equilibrium involving domestic transfers only depends on an existence proof, for example. Comparable proofs for free trade areas have not been provided to date because unharmonized tariffs imply goods prices that vary by member country and require potentially complicated rules of origin that block standard proofs. This paper fills this gap by providing the missing proof that starting from an arbitrary world trade equilibrium, a free trade area equilibrium can be found involving domestic transfers only that is at least as satisfactory for every consumer as the original allocation.