Result R4806: Equivalent characterisations of gaussian random euclidean real numbers shows that every real-linear combination of the components of $X$ is a basic real gaussian. Thus, for example, the linear combination \begin{equation} e_d \cdot X = X_d \end{equation} is a basic real gaussian, where $e_d = (0, \ldots, 1, \ldots, 0)$ is the standard basis vector in $\mathbb{R}^D$ which has all components $0$ except the $d$th component, which equals $1$. The claim follows. $\square$