# Definition:Bound Variable/Examples/Universal Statement

## Definition

In the universal statement:

$\forall x: P \paren x$

the symbol $x$ is a bound variable.

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

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