What does \forall (∀) actually mean in a signature?

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From the bits and pieces of information I gathered about agda I'd (apparently erroneously) concluded that ∀ {A} was equivalent to {A : Set}. Now I noticed that

flip : ∀ {A B C} -> (A -> B -> C) -> (B -> A -> C)

is invalid (something about Set\omega which in turn seems to be some internal something, but

flip : {A B C : Set} -> (A -> B -> C) -> (B -> A -> C)

is fine. Can anyone clear this up for me?

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