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If a structure $\mathcal{A}$ satisfies a set of formulas $\Phi$, then for $\phi\in \Phi$, does $\mathcal{A} \models \phi [\alpha]$ for all assignments $\alpha$?

I apologize if this question may be very vague. I'm just studying predicate logic right now.

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    $\begingroup$ Unless I'm missing something, that's exactly what "$\mathcal{A}\models\phi$" means in the first place when $\phi$ has free variables. $\endgroup$ – Noah Schweber Nov 15 '18 at 0:44

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