Using the Fitch application and only Intro and Elim rules (& REIT if necessary), prove that $$\forall x \forall y (P(x) \implies Q(y)) \iff (\exists x P(x) \implies \forall y Q(y))$$ is a logical truth (i.e. prove it from no premises)
I am attaching a screenshot of my work so far, please give me feedback and/or assistance so that I can fix or finish this proof. I am currently stuck and don't know if what I did is right or not because I don't know what to do next. Any feedback is appreciated. Thanks.