What i'm essentially asking is if the following statement is true:
$ \forall x \exists y (R(x) \lor Q(y)) :\Leftrightarrow \exists y \forall x (R(x) \lor Q(y)) $
where $:\Leftrightarrow $ means that the two statements are logically equivalent.
(sometimes $\vDash$ and it's mirror are used for logical equivalence but can't find the mirrored symbol in mathjax
Edit: I suspect that it is not true but i'm trying to prove it and seems it should be.