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Put yet another way, this says that the single statement

\begin{equation*} \exists y \forall x P(x,y) \imp \forall x \exists y P(x,y) \end{equation*}

is always true. This is sort of like a tautology, although we reserve that term for necessary truths in propositional logic. A statement in predicate logic that is necessarily true gets the more prestigious designation of a law of logic (or sometimes logically valid, but that is less fun).

in-context