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Let X be a nonempty partially ordered domain of objects. Define externality between two objects as the existence of a part belonging to one but not the other. Under reflexivity and antisymmetry, externality is equivalent to inequality. The axiom of universal non-externality therefore entails that all elements of X are identical. Nonemptiness then implies that X contains exactly one element, denoted W. The result is a conditional mathematical theorem under the stated axioms.