It's easier to explain the question on an example. Let's consider this pretty simple problem:
We have to prove that $(-1)a=-a$ where $a \in R $.
My question is, can I prove this in the following way?
$$(-1)a\stackrel{?}{=}-a \Rightarrow (-1)a+a\stackrel{?}{=}0 \Rightarrow \\ a(-1+1)\stackrel{?}{=}0 \Rightarrow a*0\stackrel{?}{=}0 \Rightarrow 0=0 $$
Is this a correct proof?
Since we arrived to an obvious truth from uncertainty, can we conclude the problem proven?