Is it okay to mix $\iff$ and $\implies$ in a single derivation?

Question

Say, I have to write down the steps to solve this equation $$ \frac{1 + ax}{a} - x = \frac{1}{a^2}(x - a). $$

Is the following manner a good way to write it?

\begin{align*} \frac{1 + ax}{a} - x = \frac{1}{a^2}(x - a) & \iff \frac1a = \frac1{a^2} (x - a) \\ & \implies a = x - a \\ & \iff x = 2a. \end{align*}

The reason I went for $ \implies $ at the second step because we cannot divide $ a^2 $ on both sides of $ a = x - a $ to get the preceding step $ \frac1a = \frac1{a^2} (x - a) $ when $ a = 0 $.

Is it valid to mix $ \iff $ and $ \implies $ in a single derivation like this?

Answer 1

It’s okay if and only if every equivalence or implicication arrow is aligned and put on a separate line, like you did. This way, it will intuitively be understoood as a chain of equivalences or implications.

Not okay: “$A ⇔ B ⇒ C$” – now, did you maybe mean “$A ⇔ (B ⇒ C)$” or is it a chain?