# Show that if $x$ does not occur free in $α$, then $α \vDash ∀ x α$.

On page 99, A Mathematical Introduction to Logic, Herbert B. Enderton（2ed),

Show that if $x$ does not occur free in $α$, then $α \vDash ∀ x α$.

Added:This could be seen as a follow-up problem of this one. Frankly speaking, I'm totally confused between this problem and the answer to that problem.

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"$\vDash$" means that RHS is true in every model of LHS. If $x$ does not occur free in $\alpha$, a model of $\alpha$ need not assign a value to $x$ - that is, in a model of $\alpha$, $\alpha$ is true for all assignments of $x$, so $\alpha \vDash \forall x \alpha$.