Transposition (logic) - Formal Notation

Formal Notation

The transposition rule may be expressed as a sequent:

where is a metalogical symbol meaning that is a syntactic consequence of in some logical system;

or as a rule of inference:

where the rule is that wherever an instance of "" appears on a line of a proof, it can be replaced with "";

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:

where and are propositions expressed in some formal system.