$2x = 2y \Rightarrow x = y$ with $x,y \in \mathbb{Z}$ How can I show, $2x = 2y \Rightarrow x = y$ with $x,y \in \mathbb{Z}$, when I can only use elements out of $\mathbb{Z}$? It is $\frac{1}{2} \notin \mathbb{Z}$, so I can't multiply both sides with $\frac{1}{2}$. How can I prove it?

$$2x=2y \Leftrightarrow 2x-2y=0 \Leftrightarrow 2(x-y)=0$$
