Disjunction elimination
Rule of inference of propositional logic
In propositional logic, 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 from a logical proof. It is the inference that if a statement
P
{\displaystyle P}
implies a statement
Q
{\displaystyle Q}
and a statement
R
{\displaystyle R}
also implies
Q
{\displaystyle Q}
, then if either
P
{\displaystyle P}
or
R
{\displaystyle R}
is true, then
Q
{\displaystyle 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.
An example in English:
1. If I'm inside, I have my wallet on me.
2. If I'm outside, I have my wallet on me.
3. It is true that either I'm inside or I'm outside.
Therefore, I have my wallet on me.
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This entry incorporates text from “Disjunction elimination” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.