This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 ForAll ForAll[x, expr] represents the statement that expr is True for all values of x. ForAll[x, cond, expr] states that expr is True for all x satisfying the condition cond. ForAll[, , ... , expr] states that expr is True for all values of all the . ForAll[x, expr] can be entered as . The character can be entered as fa or \[ForAll]. The variable x is given as a subscript. ForAll[x, cond, expr] can be entered as . In StandardForm, ForAll[x, expr] is output as . ForAll[x, cond, expr] is output as . ForAll can be used in such functions as Reduce, Resolve and FullSimplify. The condition cond is often used to specify the domain of a variable, as in x Integers. ForAll[x, cond, expr] is equivalent to ForAll[x, Implies[cond, expr]]. ForAll[, , ... , ... ] is equivalent to . The value of x in ForAll[x, expr] is taken to be localized, as in Block. See Section 3.4.11. See also: Exists, Resolve, Reduce, Element, Blank, SolveAlways. New in Version 5.0.