"Consider the equivalence
∀x∃yφ(x, y) ↔ ∃y∀x φ(x, y)
You can assume that φ has no free variables other than x and y.
Show that one direction of this equivalence is valid (i.e. true in every structure/model). Prove this carefully."
I have found out that the direction to the "left" is valid.
So I am sure that this is valid: ∃y∀x φ(x, y) → ∀x∃yφ(x, y)
Now I have to prove it by showing that it's true in every structure/model.
Can someone show me how this kind of proof is done?