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Reference.org
Universal generalization
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<p>In <a href="/facts/Predicate_logic/lcISqWIg">predicate logic</a>, generalization (also universal generalization, universal introduction, GEN, UG) is a <a href="/facts/Validity_(logic)/oMGkywGC">valid</a> <a href="/facts/Rule_of_inference/QV5NklQ9">inference rule</a>. It states that if ⊢ P ( x ) {\displaystyle \vdash \!P(x)} has been derived, then ⊢ ∀ x P ( x ) {\displaystyle \vdash \!\forall x\,P(x)} can be derived. </p>