Is “implies” the best symbol when rewriting equations

Question

In my mathematical homework, I usually indicate algebraic rewrites of equations using implication, and the symbol "$\implies$" (LaTeX \implies). For instance, I might write $$ 3 x – y = 0 \implies 3 x = y \implies x = \frac{y}{3} $$ to mean that, since $3 x – y = 0$, the equivalent equation $3 x = y$ is also true, which then indicates that $x = y/3$ is true. Is logical implication the correct facility to express rewriting an equation into an equivalent form? If not, what other concept and symbol would be correct here?

Answer 1

Another symbol which you can use is the "if and only if" symbol, in $\rm\LaTeX$, it is $\iff$ and is denoted by $\iff$(Also pointed out by @StefanOctavian)

So your equation re-write thus becomes : $$\begin{align} 3x-y=0 &\iff 3x = y\\ &\iff x = \frac{y}{3} \end{align}$$