Description: Extend wff definition to include the universal quantifier ("for all").
A. x ph is read " ph (phi) is true for all x ". Typically,
in its final application ph would be replaced with a wff containing
a (free) occurrence of the variable x , for example x = y . In
a universe with a finite number of objects, "for all" is equivalent to a
big conjunction (AND) with one wff for each possible case of x .
When the universe is infinite (as with set theory), such a
propositional-calculus equivalent is not possible because an infinitely
long formula has no meaning, but conceptually the idea is the same.