Database: Statements entailing their own negation

Proposition 52: Statements entailing their own negation (inference rule)

Given that \phi entails its negation \neg \phi , we may infer that \neg \phi holds: \cfrac{\phi \vdash \neg \phi}{\vdash \neg \phi}.

Proof: By the identity rule, \phi entails \phi . Then, by negation introduction, we infer \neg \phi holds. \square

This database entry builds on the following:

  1. Terminology: Inference, entailment
  2. Terminology: Inference rule
  3. Definition: Negation
  4. Theorem: The identity rule
  5. Inference rule: Negation introduction