Function Obtained by Substitution from URM Computable Functions

Theorem
Let the functions $$f: \N^t \to \N, g_1: N^k \to \N, g_2: N^k \to \N, \ldots, g_t: N^k \to \N$$ all be URM computable functions.

Let $$h: \N^k \to \N$$ be defined from $$f, g_1, g_2, \ldots, g^t$$ by substitution.

Then $$h$$ is also URM computable.