Definition:Existential Statement

Definition
An existential statement is one which expresses the existence of at least one object (in a particular universe of discourse) which has a particular property.

That is, a statement of the form:
 * $\exists x: P \left({x}\right)$

where:
 * $\exists$ is the existential quantifier
 * $P$ is a predicate symbol.

It means:
 * There exists at least one $x$ (in some given universe of discourse) which has the property $P$.

Also see

 * Universal Statement

Dummy Variable
In the expression $\exists x: P \left({x}\right)$, the symbol $x$ is known as a dummy variable, or 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.