Squeeze Theorem for Real Sequences/Corollary

Corollary to Squeeze Theorem for Sequences
Let $\left \langle {y_n} \right \rangle$ be a sequence in $\R$ which is null, that is:
 * $y_n \to 0$ as $n \to \infty$

Let:
 * $\forall n \in \N: \left|{x_n - l}\right| \le y_n$

Then $x_n \to l$ as $n \to \infty$.

Proof
From the corollary to Negative of Absolute Value, we have:
 * $\left|{x_n - l}\right| \le y_n \iff l - y_n \le x_n \le l + y_n$

From the Combination Theorem for Sequences: Sum Rule:
 * $l - y_n \to l$ as $n \to \infty$

and:
 * $l + y_n \to l$ as $n \to \infty$

So by the Squeeze Theorem for Sequences, $x_n \to l$ as $n \to \infty$.