## Quick Smooth Manifold Question

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!