Real numbers/Sequences/Squeeze criterion/Fact/Proof/Exercise

Let ${\left(x_n\right)}_{n\in \mathbb{N}},{\left(y_n\right)}_{n\in \mathbb{N}}$ and ${\left(z_n\right)}_{n\in \mathbb{N}}$ be three real sequences. Let $x_n\le y_n\le z_n$ for all $n\in \mathbb{N}$ and ${\left(x_n\right)}_{n\in \mathbb{N}}$ and ${\left(z_n\right)}_{n\in \mathbb{N}}$ be convergent to the same limit $a$. Prove that also ${\left(y_n\right)}_{n\in \mathbb{N}}$ converges to the same limit $a$.

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