Transposition (logic)

In propositional logic, transposition is a valid rule of replacement that permits one to switch the antecedent with the consequent of a conditional statement in a logical proof if they are also both negated. It is the inference from the truth of "A implies B" to the truth of "Not-B implies not-A", and conversely. It is very closely related to the rule of inference modus tollens. It is the rule that

Transposition

Type	Rule of replacement
Field	Propositional calculus
Statement	The inference from the truth of "A implies B" to the truth of "Not-B implies not-A"
Symbolic statement	${\displaystyle (P\to Q)\Leftrightarrow (\neg Q\to \neg P)}$

where "${\displaystyle \Leftrightarrow }$" is a metalogical symbol representing "can be replaced in a proof with".