bimodules in a biclosed category

Has anyone proved that if you take an "algebra" (actually monoid) object in a monoidal biclosed category that has equalizers and coequalizers, then the category of two-sided modules for that algebra is again a monoidal biclosed category. Mac Lane did this in 1965 when everything is symmetric (the tensor, the algebra and the modules) under the (surely irrelevant) assumption that the original category is also abelian. The fact is certainly true, but writing down the proof would be rather painful. Michael Barr