---
tag: FTH70E7K1D
kind: concept
name: Disjunction elimination
sources:
  - wikipedia: en:8529@r1312422497
    locator: Disjunction elimination
    note: adopted
    mention: wikipedia://en/8529
    sections: [Summary]
same_as:
  wikidata: Q5282265
  wikipedia: Disjunction elimination
inventory: [DF6MK39A3B]
---

## Summary

In [[propositional logic|09K9MWD2QQ]], **disjunction elimination** (sometimes named **proof by cases**, **case analysis**, or **or elimination**) is the valid argument form and rule of inference that allows one to eliminate a [[disjunctive statement|0F72FK8EKB]] from a logical proof. It is the inference that if a statement $P$ implies a statement $Q$ and a statement $R$ also implies $Q$, then if either $P$ or $R$ is true, then $Q$ has to be true. The reasoning is simple: since at least one of the statements P and R is true, and since either of them would be sufficient to entail Q, Q is certainly true.