I have $x$ and $y$ transcendental over a field extension $E/K$, and I have to prove (or disprove) that $\left \{x,y\right \}$ is algebraically independent.
I was able to prove that $\left \{x',y'\right \}$ is algebraically independent over $K$ if $x'$ is transcendental over $K$ and $y'$ is transcendental over $K(x')$ (not $K$). Maybe if I could prove that $y$ is transcendental over $K(x)$ I would be done, but I do not know how to prove it. Maybe that it is not even true.