bound variable

If a is any individual variable and α is any wff, every occurrence of a in α is said to be bound (by the quantifiers) when occurring in the wffs (∀a)α and (∃a)α. Any occurrence of a variable that is not bound is said to be free. Thus, in (∀x)(ϕx…

…is known as relettering a bound variable. If β is the result of relettering a bound variable in a wff α, then α and β are said to be bound alphabetical variants of each other, and bound alphabetical variants are always equivalent. The reason for restricting the replacement variable to…

…x is here called a bound (individual) variable. Its values are supposed to be members of some fixed class of entities, called individuals, a class that is variously known as the universe of discourse, the universe presupposed in an interpretation, or the domain of individuals. Its members are said to…