Modus ponendo tollens
Transformation rules 

Propositional calculus 
Rules of inference 
Rules of replacement 

Predicate logic 
Modus ponendo tollens (Latin: "mode that by affirming, denies")^{} is a valid rule of inference for propositional logic, sometimes abbreviated MPT.^{} It is closely related to modus ponens and modus tollens. It is usually described as having the form:
 Not both A and B
 A
 Therefore, not B
For example:
 Ann and Bill cannot both win the race.
 Ann won the race.
 Therefore, Bill cannot have won the race.
As E.J. Lemmon describes it:"Modus ponendo tollens is the principle that, if the negation of a conjunction holds and also one of its conjuncts, then the negation of its other conjunct holds."^{}
In logic notation this can be represented as:
Based on the Sheffer Stroke (alternative denial), "", the inference can also be formalized in this way: