Modus ponens

In propositional logic, modus ponens (; MP), also known as modus ponendo ponens (from Latin 'mode that by affirming affirms'), conditional elimination, implication elimination, or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "P implies Q. P is true. Therefore, Q must also be true." Modus ponens is a mixed hypothetical syllogism and is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of modus ponens. The history of modus ponens goes back to antiquity. The first to explicitly describe the argument form modus ponens was Theophrastus. It, along with modus tollens, is one of the standard patterns of inference that can be applied to derive chains of conclusions that lead to the desired goal.