Let $Z \in \mathsf{N}(0, 1)$ be a D211: Standard gaussian random real number.
Let $X_0, X_1, X_2 \in \mathsf{Random}(\mathbb{R})$ each be a D3161: Random real number such that

(i)	\begin{equation} X_0 : = Z \end{equation}
(ii)	\begin{equation} X_1 : = Z \end{equation}
(iii)	\begin{equation} X_2 : = - Z \end{equation}

Let $a \in \mathbb{R}$ be a D993: Real number.

Since $X_0 : = Z = : X_1$, then clearly $X_0$ and $X_1$ agree in distribution. Furthermore, result R3923: Standard gaussian random real number is symmetric about zero implies that \begin{equation} X_2 : = - Z \overset{d}{=} Z = : X_1 \end{equation} This establishes the first claim. Next \begin{equation} \begin{split} \mathbb{P}(X_0 \leq a, X_1 \leq a) & = \mathbb{P}(Z \leq a, Z \leq a) \\ & = \mathbb{P}(\{ Z \leq a \} \cap \{ Z \leq a \}) \\ & = \mathbb{P}(\{ Z \leq a \}) \\ & = \mathbb{P}(Z \leq a) \\ & = \mathbb{P}(Z \in (-\infty, a]) \\ & \neq \mathbb{P}(Z \in [-a, a]) \\ & = \mathbb{P}(- a \leq Z \leq a) \\ & = \mathbb{P}(Z \leq a, Z \geq -a) \\ & = \mathbb{P}(Z \leq a, - Z \leq a) \\ & = \mathbb{P}(X_1 \leq a, X_2 \leq a) \end{split} \end{equation} $\square$