Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$X, Y : \Omega \to \Xi$ are each a D202: Random variable on $P$
(ii)	\begin{equation} \mathbb{P}(X = Y) = 1 \end{equation}
(iii)	$\{ X \in E \}, \{ Y \in E \} \in \mathcal{F}$ are each an D1716: Event in $P$

Then \begin{equation} \mathbb{P}(X \in E) = \mathbb{P}(Y \in E) \end{equation}