Definition:Universal Statement

A universal statement is one which expresses the fact that all objects (in a particular universe of discourse) have a particular property.

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

where:
 * $$\forall$$ is the universal quantifier;
 * $$P$$ is a predicate symbol.

It means: "All $$x$$ (in some given universe of discourse) have the property $$P$$."

Note that if there exist no $$x$$ in this particular universe, $$\forall x: P \left({x}\right)$$ is always true: see vacuous truth.