Consider the following proof by contradiction. We want to prove that $\sqrt{2}$ is irrational. We assume $\sqrt{2} = \frac{p}{q}$ where $p, q \in \mathbb{Z}$ and $\gcd(p,q)=1$. We then derive that $2$ divides both $p$ and $q$, which contradicts $\gcd(p,q)=1$. Which rule of inference in classical logic justifies this proof structure?