Definition:Existential Statement

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 $$P$$."