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.