The full subcategory of representable controvariant functors

Let $\mathcal{C}$ be a category, let's denote by $\operatorname{Set}^{\mathcal{C}^{\operatorname{op}}}$ the category of presheaves of sets defined on $\mathcal{C}$ and natural transformations.

I want to prove that $\mathcal{C}$ is isomorphic (or at least equivalent) to the full subcategory of $\operatorname{Set}^{\mathcal{C}^{\operatorname{op}}}$ given by representable functors.

The only things i know are:

1) Yoneda embedding is fully faithful;

2) Yoneda embedding is injective on objects;

3) Yoneda's Lemma.

Do you think i can prove what I want using 1), 2), 3)? Could you suggest me how?

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Well you should know that in order to be an equivalence of category it's necessary and sufficient for a functor $F$ to be fully faithful and that each object of the target category is isomorphic to $FA$ for a suitable $A$ in the source category. This is definitely your case.
That fact gives you that $\mathcal{C}$ is actually isomorphic to a full subcategory of $Set^{C^{op}}$, namely the one made of the hom-functors. –  Edoardo Lanari Jun 21 '13 at 13:04