Why is this statement true in probability/statistics? 
$P(X_n \leq X, |X_n - X|< \epsilon) \leq P(X \leq X + \epsilon)$ because $X_n - \epsilon < X < X_n + \epsilon < X + \epsilon$

For the right side of the equality...since we are not restricting X to be greater than $X_n - \epsilon$, can't the right side be less sometimes? Why is this statement true?
Thanks in advance  

Maybe you wanted $P(X_n≤X,|X_n−X|<\varepsilon)≤P(X≤X_n+\varepsilon)$? This is a little bit less trivial, since the right-hand-side might be smaller than $1$, and also true. Because any $\omega\in\Omega$ that satisfies $X_n(\omega)−\varepsilon<X(\omega)<X_n(\omega)+\varepsilon<X(\omega)+\varepsilon$ will also satisfy $X(\omega)≤X_n(\omega)+\varepsilon$, so that
$\{X_n≤X,|X_n−X|<\varepsilon\}\subseteq\{X≤X_n+\varepsilon\}$.
