Chapter 2.2, Problem 23E

Let $x$ and $y$ be integers, and let $m$ and $n$ be positive integers. Use mathematical induction to prove the statements in Exercises $18-23$. $($ The definitions of $x^n$ and $nx$ are given before Theorem $2.5$ in Section $2.1$ $)$

$\mathrm{}m\left(nx\right)=\left(mn\right)x$