In predicate calculus, a universal formula is a prenex normal form formula (i.e., a formula written as a string of quantifiers and bound variables followed by a quantifier-free part) in which the quantified variables are universally quantified. Every universal formula is logically equivalent to the negation of some existential formula (and vice-versa). When there are no free variables (i.e., when all the variables are bound) in a universal formula, it is called a universal sentence.

existential formula | universal quantifier