I have working on this formula $(\forall x \exists y (P(x) \supset Q(y))) \supset (\exists y \forall x (P (x) \supset Q(y)))$ to either prove or disprove it.
First, I tempted to disprove it, but I changed my mind.
I wrote down "for all x that there exists some y satisfies corresponding condition", and "there exists some y that for all x satisfies corresponding condition." I think these statements refer to the same idea.
Any suggestions?