Editing Universal generalization (section)

{{Short description|Rule of inference in predicate logic}}
{{more footnotes|date=March 2023}}
{{Infobox mathematical statement
| name = Universal generalization
| type = [[Rule of inference]]
| field = [[Predicate logic]]
| statement = Suppose <math>P</math> is true of any arbitrarily selected <math>p</math>, then <math>P</math> is true of everything.
| symbolic statement = <math>\vdash \!P(x)</math>, <math>\vdash \!\forall x \, P(x)</math>
}}
{{Transformation rules}}

In [[predicate logic]], '''generalization''' (also '''universal generalization''', '''universal introduction''',<ref>Copi and Cohen</ref><ref>Hurley</ref><ref>Moore and Parker</ref> '''GEN''', '''UG''') is a [[Validity (logic)|valid]] [[rule of inference|inference rule]]. It states that if <math>\vdash \!P(x)</math> has been derived, then <math>\vdash \!\forall x \, P(x)</math> can be derived.