Rule of replacement

Transformation rules
Propositional calculus
Rules of inference
Modus ponens / Modus tollens Biconditional introduction / elimination Conjunction introduction / Simplification Disjunction introduction / elimination Disjunctive / Hypothetical syllogism Constructive / Destructive dilemma Absorption Modus ponendo tollens
Rules of replacement
Associativity Commutativity Distributivity Double negation De Morgan's laws Transposition Material implication Exportation Tautology Negation introduction
Predicate logic
Universal generalization / instantiation Existential generalization / instantiation

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.

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