Function spectrum with values in a ring spectrum

If $E$ is a ring spectrum, then $F(X_{+},E)$ is a ring spectrum. Its multiplication is adjoint to evaluating the two functions on the two copies supplied by the diagonal of $X$, then multiplying in $E$. Its unit is the constant unit function. Coassociativity of the diagonal and associativity in $E$ prove the associative identity; the counit and unit identities prove both unit laws.