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 $$P$$."

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.