Rule of replacement

In logic, a rule of replacement[1][2][3] is a transformation rule that may be applied to only a particular segment of an expression. A logical system may be constructed so that it uses either axioms, rules of inference, or both as transformation rules for logical expressions in the system. Whereas a rule of inference is always applied to a whole logical expression, a rule of replacement may be applied to only a particular segment. Within the context of a logical proof, logically equivalent expressions may replace each other. Rules of replacement are used in propositional logic to manipulate propositions.

Common rules of replacement include de Morgan's laws, commutation, association, distribution, double negation,[4] transposition, material implication, material equivalence, exportation, and tautology.


  1. Copi, Irving M.; Cohen, Carl (2005). Introduction to Logic. Prentice Hall.
  2. Hurley, Patrick (1991). A Concise Introduction to Logic 4th edition. Wadsworth Publishing.
  3. Moore and Parker
  4. not admitted in intuitionistic logic

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