This is probably an easy question. Let C be a category with (finite) products. An internal hom in C category is an object uhom(X, Z) which represents the functor:

Y |-----> hom(Y x X, Z)

here "uhom" is for "underlined hom" as that is how it is commonly denoted. Many example of categories with internal homs satisfy an a priori stronger for of adjunction:

uhom(Y x X. Z) = uhom(Y, uhom(X,Z))

Is this automatic for categories with internal homs? Is there an easily understood counter example?

(*) This might not be the most general/best definition of internal hom, but it is valid for many examples.