Bound Variable/Examples/Existential Statement

Definition
In the existential statement:
 * $\exists x: P \left({x}\right)$

the symbol $x$ is a bound variable.

Thus, the meaning of $\exists x: P \left({x}\right)$ does not change if $x$ is replaced by another symbol.

That is, $\exists x: P \left({x}\right)$ means the same thing as $\exists y: P \left({y}\right)$ or $\exists \alpha: P \left({\alpha}\right)$. And so on.

Also see

 * Definition:Bound Variable/Examples/Universal Statement