What does the universal quantifier ∀x express?

In the philosophy of logic, the universal quantifier, symbolized as $\forall x$, is a logical operator used to assert that a given formula holds true for every value of the specified variable within a domain.12

When applied to a propositional function $\varphi x$, the expression $(\forall x)\varphi x$ is read as "For all $x$, $x$ is $\varphi$" or, more simply, "Everything is $\varphi$."3

The universal quantifier is fundamental to the predicate calculus, where it allows for the expression of general statements. It is often connected to the existential quantifier ($\exists x$) through the principle of duality: asserting that everything has a certain property is logically equivalent to denying that there is something that lacks that property. Consequently, in many formal systems, one quantifier can be defined in terms of the other using negation.23