A universal statement applies to every element of its universe. Universal specification is the rule that allows us to use such a statement for a particular object. This rule is the bridge between quantified premises and ordinary propositional inference rules such as Modus Ponens, Modus Tollens, Hypothetical Syllogism, and Disjunctive Syllogism. In this lesson, universal specification in quantified arguments is used to test validity and identify common conditional errors.

The Rule of Universal Specification states that if an open statement is true for every element of a universe, then it is true for each particular element of that universe. If $a$ is a specific element of the universe and $\forall x\,p(x)$ is true, then $p(a)$ is true.