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.

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

[4] The "Tautology" column shows how to interpret the notation of a given rule.