How does embedding "there exists" (∃) and "for all" (∀) work?

Question

I'm wondering how embedding works for "there exists" (∃) and "for all" (∀) in predicate calculus. Specifically, I'm trying to use existential instantiation (EI) and existential generalization (EG) to formally show that ∃x∃y(R(x,y)) --> ∃y∃x(R(x,y)).

Not looking for the whole proof. But some hints as to how embedding works with these entities (and how to get started with the proof) would be a huge help!

Thanks in advance.

Answer 1

The statement reads "For some x and some y, if there is a relationship between them, then we can deduce that there is a relationship between some x and some y".

Hope that helps a bit