Modus ponens

Summary

Modus ponens is the rule of inference that gets $q$ from the two premises $p$ and $p \to q$. $$\frac{p \qquad p \to q}{q}$$ It is valid: when the two premises are true, the conclusion $q$ is true.

Remarks

Most proof systems for propositional logic use modus ponens as a rule. Its partner modus tollens gets $\neg p$ from $\neg q$ and $p \to q$.

Explanations

L1 human

Modus ponens is the most common step in a proof. If you know that $n$ is divisible by $4$, and that each number divisible by $4$ is even, then you know that $n$ is even.