The strictification theorem for monoidal categories states that every monoidal categorically is monoidally equivalent to a strict monoidal category. Is there a strictification theorem for closed monoidal categories? I expect this to take a form similar to the following.

Call a closed monoidal category strict if the monoidal structure is strict and the following canonical isomorphisms are identities: $$[I, X] \cong X$$ $$[X, [Y, Z]] \cong [X \otimes Y, Z]$$

I believe that the first identity should follow from a strictification theorem for closed categories, so that the strictification theorem for closed monoidal categories is the union of the strictification theorems for monoidal categories, closed categories, along with the addition axiom governing the interaction between the monoidal and closed structures given by currying.

This seems like a natural question to ask, and so I would not be surprised to find it in the literature already, but I have not been able to do so.