The following theorem has the form of an implication.
If n is an integer and 3n+2 is even, then n is even.
Give a direct proof of this theorem without using contradiction.
Since $\displaystyle 3n+2$ is even we may state WLOG that $\displaystyle 3n+2=2z\implies 3n=2(z-1)$ and since $\displaystyle 2\nmid 3$ it must be true that $\displaystyle 2\mid n$. The conclusion follows.