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.