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High Quality Content by WIKIPEDIA articles! In predicate logic, universal quantification formalizes the notion that something (a logical predicate) is true for everything, or every relevant thing. The resulting statement is a universally quantified statement, and we have universally quantified over the predicate. In symbolic logic, the universal quantifier (typically forall, , a turned a) is the symbol used to denote universal quantification, and is often informally read as "given any" or "for all".