# 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.

Transformation rules |
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Propositional calculus |

Rules of inference |

Rules of replacement |

Predicate logic |

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

## References

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