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  "body": "\n## Summary\n\nIn [[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.\n",
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