Corollary

— Let $s_1, s_2, \ldots, s_n$ be the elementary symmetric polynomials in $X_1, \ldots, X_n$. For every rational fraction $g \in K(S_1, S_2, \ldots, S_n)$ the sequence $(s_1, s_2, \ldots, s_n)$ is substitutable in $g$ and the mapping $g \mapsto g(s_1, s_2, \ldots, s_n)$ is an isomorphism of $K(S_1, S_2, \ldots, S_n)$ onto the field of symmetric rational fractions in $X_1, \ldots, X_n$.

This follows from Prop. 2 and Th. 1 of IV, p. 62.