10. If $\alpha_1,..., \alpha_n$ are $\mathbb{Q}$-linearly independent algebraic integers in $\mathbb{Q}(\theta)$, and if
$$\Delta[\alpha_1,..., \alpha_n] = d$$
where $d$ is the discriminant of $\mathbb{Q}(\theta)$, show that $\{\alpha_i,..., \alpha_n\}$ is an integral basis for $\mathbb{Q}(\theta)$.
