Product (Category Theory) is Unique

Theorem
Let $\mathbf C$ be a metacategory.

Let $A$ and $B$ be objects of $\mathbf C$.

Let $A \times B$ and $A \times' B$ both be products of $A$ and $B$.

Then there is a unique isomorphism $u: A \times B \to A \times' B$.

That is, products are unique up to unique isomorphism.