Modus ponens

Modus ponens

Type	Deductive argument form Rule of inference
Field	Classical logic Propositional calculus
Statement	${\displaystyle P}$ implies ${\displaystyle Q}$. ${\displaystyle P}$ is true. Therefore, ${\displaystyle Q}$ must also be true.
Symbolic statement	${\displaystyle P\to Q,\;P\;\vdash \ Q}$

In propositional logic, modus ponens (/ˈmoʊdəs ˈpoʊnɛnz/; MP), also known as modus ponendo ponens (from Latin 'method of putting by placing'),^[1] implication elimination, or affirming the antecedent,^[2] is a deductive argument form and rule of inference.^[3] 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.^[4] The first to explicitly describe the argument form modus ponens was Theophrastus.^[5] 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.