I have to prove a statement $$\forall x\exists y\left ( \Phi \left ( x \right )\vee \Psi \left ( y \right ) \right ) \vdash \exists y\forall x \left ( \Phi \left ( x \right )\vee \Psi \left ( y \right ) \right )$$ (the variable $y$ has no occurrences in formulas $\Phi \left ( x \right )$, $\Psi \left ( x \right )$).
Using rules of calculus, i got this one $$\left ( \Phi \left ( y \right )\vee \Psi \left ( y \right ) \right ) \vdash \left ( \Phi \left ( x \right )\vee \Psi \left ( x \right ) \right )$$
But this is not all isn't it?
I think, that I have to use the fact about $y$ here, but I don't how..
I have to do a formal proof, using this rules
