Corollary

*Let $L$ be a separable finitely generated extension of $K$ and let $S$ be a subset of $L$ such that $L = K(S)$. Then there exists a separating transcendence basis $B$ of $L$ over $K$, contained in $S$.

Since $\Omega_K(L)$ is generated by the differentials of the elements of $S$, there exist $s$ elements $x_1, \ldots, x_s$ of $S$ such that $(dx_1, \ldots, dx_s)$ is a basis of $\Omega_K(L)$ over $L$. Now it suffices to apply Th. 5.