We all know if there is $$p\Rightarrow q$$
We must prove from $p$ and manipulate it with little algebra until get $q$ right? (In this case, just forget about reductio ad absurdum and contraposition, cz i wanna use classic way) I mean we go from $p$ to $q$
But what if we meet a different case. When the case is just prove p.
For example:
Prove $(an+b)m\equiv bm\pmod{n}$
There is no information about those variable are. Just assume that they are integers.
So, what i did is:
$$\begin{align} (an+b)m &\equiv bm\pmod{n}\\ &\iff n|[(an+b)m]-bm\\ &\iff n|anm\\ &\iff n|nam \tag {true} \end{align} $$
But i don't think that this's correct. Because i go from $p$. But $p$ is not yet proved or unkown.
Please do a correction if there are mistakes.. Thanks.