Permutation_of_Variables_of_Primitive_Recursive_Function

Let $f: \N^k \to \N$ be a primitive recursive function. Let $\sigma$ be a permutation of $\left({1, 2, \ldots, k}\right)$. Then the function $h: \N^k \to \N$ defined as $h \left({n_1, n_2, \ldots, n_k}\right) = f \left({n_{\sigma \left({1}\right)}, n_{\sigma \left({2}\right)}, \ldots, n_{\sigma \left({k}\right)}}\right)$ is also primitive recursive.