group theory - How to prove basic properties that follow from the axioms of a field?

I am recently learning about fields and frequently get stuck whole trying to prove some properties that drop out of the axioms. I'll give an example to try and see how too go about doing it.

Let $m,n \in \mathbb{F}$ some field. Then prove $(-m)n=-(mn)=-mn$. Now I know $(-m)$ is the unique element of the field such that $(-m)+m=0$ and $-mn$ is the unique element of the field such that $(-mn)+mn=0$

I have so far done $(-m)n=(-m1)n=(-1\cdot(mn))=-1\cdot (mn)$ but I don't know how to just write this is $=-(mn).$