structural:expansion, structural:scholar_edition
Modus ponens

Modus ponens (also known as "affirming the antecedent" or "the law of detachment") is the primary deductive rule of inference. It applies to arguments that have as first premise a conditional statement (P → Q {\displaystyle P\rightarrow Q}) and as second premise the antecedent (P {\displaystyle P}) of the conditional statement. It obtains the consequent (Q {\displaystyle Q}) of the conditional statement as its conclusion. The argument form is listed below:

In this form of deductive reasoning, the consequent (Q {\displaystyle Q}) obtains as the conclusion from the premises of a conditional statement (P → Q {\displaystyle P\rightarrow Q}) and its antecedent (P {\displaystyle P}). However, the antecedent (P {\displaystyle P}) cannot be similarly obtained as the conclusion from the premises of the conditional statement (P → Q {\displaystyle P\rightarrow Q}) and the consequent (Q {\displaystyle Q}). Such an argument commits the logical fallacy of affirming the consequent.

The following is an example of an argument using modus ponens: