Proposition Let $M_1,...,M_n$ de modules over a commutative ring $R$. If $(P,p)$ is a tensor product of $M_1,...,M_n$, then, for every multilinear function $q:M_1\times\cdot\cdot\cdot\times M_n\to Q$, there is one and only one homomorphism $h:P\to Q$ such that $q=h(p)$.
From the definition of tensor product, we know there is such homomorphism $h$.
I'm having a hard time proving its uniqueness. Does anyone have a hint?