Reflector product criterion for an exponential ideal

For a reflective subcategory $\mathcal{D}$ of a cartesian closed category $\mathcal{C}$, with reflector $L$, the subcategory $\mathcal{D}$ is an exponential ideal if and only if the canonical comparisonis an isomorphism for every $A,B$. The proof repeatedly curries a map into an object of $\mathcal{D}$ and factors it through the unit of the reflection.