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The relationship between propositions that can be derived from the definitions of connectives.

List of implication

  1. P  (P  Q) addition
  2. (P  Q)  P simplification
  3. [P  (P  Q)]  Q modus ponens
  4. [(P  Q)  ¬ Q]  ¬ P modus tollens
  5. [¬ P  (P  Q)]  Q disjunctive syllogism
  6. [(P  Q)  (Q  R)]  (P  R) hypothetical syllogism
  7. (P  Q)  [(Q  R)  (P  R)]
  8. (P  Q)  [(R  S)  [(P  R)  (Q  S)]
  9. [(P  Q)  (Q  R)  [(P  R)

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