I'm not very fluent in mathematical proofs. High School has, sadly, not taught me any kind of proof-theory. That's why I would like your help with my proof of
$$2x \bmod 3 \neq 0$$
given that $$x \bmod 3 \neq 0$$
Actually it seems absolutely logical for me, but I have no idea how to tackle the modulo for proofing. $x \in \mathbb{Z}$, if that helps.