A substitute formula for MSE I don't understand where this formula for Mean Squared Error is coming from.

How do we arrive at:

$$MSE = \frac{1}{m}||y' - y||_2^2$$

from:

$$MSE = \frac{1}{m}\cdot\sum_i(y'_{i} - y_{i})^2$$

(The source is deeplearningbook)
We have $$\|x\|_2=\sqrt{\sum_{i=1}^n x_i^2}$$

Hence $$\|x\|_2^2=\sum_{i=1}^n x_i^2$$

Now let $x=y'-y$ and you obtain your formula.