In propositional logic, tautology is one of two commonly used rules of replacement. The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are:
The principle of idempotency of disjunction:
and the principle of idempotency of conjunction:
Where "
Formal notation
Theorems are those logical formulas
The tautology rule may be expressed as a sequent:
and
where
or as a rule of inference:
and
where the rule is that wherever an instance of "
or as the statement of a truth-functional tautology or theorem of propositional logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as:
and
where