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  

If $\varepsilon$ is assumed to be non-negative then
$$
\{X\leq X+\varepsilon\}=\Omega
$$
and hence $P(X\leq X+\varepsilon)=1$ and so the inequality is trivial.
