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

 Exists Exists[x, expr] represents the statement that there exists a value of x for which expr is True. Exists[x, cond, expr] states that there exists an x satisfying the condition cond for which expr is True. Exists[, , ... , expr] states that there exist values for all the for which expr is True. Exists[x, expr] can be entered as . The character can be entered as ex or \[Exists]. The variable x is given as a subscript. Exists[x, cond, expr] can be entered as . In StandardForm, Exists[x, expr] is output as . Exists[x, cond, expr] is output as . Exists 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. Exists[x, cond, expr] is equivalent to Exists[x, cond && expr]. Exists[, , ... , ... ] is equivalent to . The value of x in Exists[x, expr] is taken to be localized, as in Block. See Section 3.4.11. See also: ForAll, FindInstance, Resolve, Reduce, Element, Eliminate. New in Version 5.0.