Is this a valid proof? Q: Prove that $m^2 = n^2$ iff (if and only if) $m = n$ or $m = -n$
I began by assuming that the condition m = n or m = -n could be restated as |m| = |n|.
Next, I rewrote that as $\sqrt{m^2} = \sqrt{n^2}$. I wrote out my argument as such:
1) $|m|  ≠ |n|$
2) $\sqrt{m^2} ≠ \sqrt{n^2}$
3) If $m^2 = n^2$, then $\sqrt{m^2} = \sqrt{n^2}$
4) Proof by contradiction  

$m^2 = n^2 \Leftrightarrow m^2 - n^2 = 0 \Leftrightarrow (m+n)(m-n) = 0 \Leftrightarrow m= \pm n$
