Proper notation for equation solving. What is the proper notation when solving one equation by inserting another known relationship?
$$y=x^2, y+2x^2=1$$$$y+2x^2=1\Leftrightarrow x^2+2x^2=1 \Leftrightarrow x=\pm\sqrt{\frac{1}{3}}$$
I assume the first $\Leftrightarrow$ is wrong since we are inserting a relationship, and the $y+2x^2=1$ equation is not logically equal to $x^2+2x^2=1$ by it self.
Edit: I guess what I'm asking is: Is there a way of notating $f(x),g(x)\Rightarrow h(x)$ cleanly?

\begin{align}&&y=x^2 \;&\text{ and }\; y+2x^2=1\\&\iff &y=x^2 \;&\text{ and }\; x^2+2x^2=1 \\&\iff &y=x^2 \;&\text{ and }\; x=\pm\sqrt{\frac{1}{3}}\\&\iff &y=\frac13 \;&\text{ and }\; x=\pm\sqrt{\frac{1}{3}}.\end{align}
