This may be stupid question, but why is it that given a topological manifold X and some atlas \mathfrak{A} then their exists a unique C^{\infty} structure \mathfrak{A}^* on X which contains \mathfrak{A}?

I can see why their exists some C^{\infty} structure. Just define \Omega to be the set of all atlases on X containing \mathfrak{A}, order it in the natural way and apply Zorn's lemma. But, why is it unique? Is it because the way one constructs the ordering any two maximal atlases \mathfrak{M},\mathfrak{N} would need to be comparable and thus equal?

Any help would be appreciated!