Negation of double universal quantifications

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In logic, when I want to negate the formula

$$\forall x \forall y( F(y) \land A(y) \to \neg G(x,y))$$

what is the correct equivalent? Intuitively, I think it gives

$$\exists x \forall y (F(y) \land A(y) \land G(x,y))$$

but I'm not to sure about it.