Does the currying of a closed abelian monoidal category preserves addition?

Question

Let $V$ be a left-closed abelian monoidal category. That is, $V$ is a left-closed monoidal category which is also an abelian category. Let $\Phi:\hom(y\otimes x,z)\to\hom(x,[y,z])$ be the currying of $V$. Then does $\Phi$ preserve addition? That is, for all morphisms $f,g:y\otimes x\to z$, does $\Phi(f+g)=\Phi(f)+\Phi(g)$ hold? This is true for the category of all right $R$-modules, where $R$ is some fixed ring.