Can someone give me a hint, how to prove that the $\Sigma$-formula
$ \neg (\psi_{x \rightarrow t} \ \& \ \exists x \psi)$
where $\psi$ is an arbitrary $\Sigma$-formula, $t$ is a $\Sigma$-term whose variable don't appear in $\psi$ and $x$ is any variable, holds in every nonempty structure ?
(What "$\psi_{x \rightarrow t}$" means and for other technical details, over which alphabet the $\Sigma$-terms etc. were defined see a different post of mine)