Dual of a monoidal closed category

Is it common knowledge that the dual of a monoidal closed category is also monoidal closed (at least in the symmetric case, but I don't think that matters). If you denote tensor by @ and hom by --o, then define a dual hom by A --x B = (A* --o B*)* and a dual tensor by A # B = (A* @ B*)* where * is the contravariant equivalence. The proof that this works is trivial. What it means is another matter entirely. Right now, I just would like to know if this is commonly known. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]