Some universal properties of the category of finite sets with regard to Cartesian closed categories were studies. The equality of any two canonical morphisms (see Mac Lane[11]) in all Cartesian closed categories is redused to the equality of a finite number of maps in the category of finite sets. Hense, a new decision algorithm for equality of canonical morphisms has been obtained. Another, result is an algorithm to decide if two ($\&$, $\supset$)-formulas $A$ and $B$ are isomorphous in all Cartesian closed categories for any values of object-variables (where $\&$ is a cartesian product and $\supset$ is an internal hom-functor). The category of finite sets is used to prove the correctness of this algorithm.