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.
Read more about this topic: Transposition (logic)
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