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

(i)	$X, A, B : \Omega \to \mathbb{R}$ are each a D3161: Random real number on $P$
(ii)	\begin{equation} \mathbb{P} \{ \omega \in \Omega : A(\omega) \leq B(\omega) \} = 1 \end{equation}

Then \begin{equation} \mathbb{P} \{ \omega \in \Omega : X(\omega) \leq A(\omega) \} \subseteq \mathbb{P} \{ \omega \in \Omega : X(\omega) \leq B(\omega) \} \end{equation}