Description: Extend wff definition to
include the universal quantifier ('for all').
is read " (phi) is true for all ." Typically, in
its final application would be replaced
with a wff containing a
(free) occurrence of the variable , for example . 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 . 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.