---
tag: BKQ3YD6SVZ
kind: concept
name: Universal generalization
aliases: [generalisation-logic, generalization-logic, universal-generalisation]
sources:
  - wikipedia: en:939333@r1316812016
    locator: Universal generalization
    note: adopted
    mention: wikipedia://en/939333
    sections: [Summary]
same_as:
  wikidata: Q5364991
  wikipedia: Universal generalization
inventory: [Q78WA34GK8]
---

## Summary

In predicate logic, **generalization** (also **universal generalization**, **universal introduction**, **GEN**, **UG**) is a valid inference rule. It states that if $\vdash \!P(x)$ has been derived, then $\vdash \!\forall x \, P(x)$ can be derived.