# Definition:Bound Variable/Examples/Existential Statement

## Definition

In the existential statement:

$\exists x: P \paren x$

the symbol $x$ is a bound variable.

Thus, the meaning of $\exists x: P \paren x$ does not change if $x$ is replaced by another symbol.

That is, $\exists x: P \paren x$ means the same thing as $\exists y: P \paren y$ or $\exists \alpha: P \paren \alpha$. And so on.