$\exists x \forall y P(x, y) \implies \forall y \exists x P(x, y)$

$\exists x \exists y P(x, y) \implies \exists y \exists x P(x, y)$

$\forall x \forall y P(x, y) \implies \forall y \forall x P(x, y)$

$\forall y \exists x P(x, y) \implies \exists x \forall y P(x, y)$