Modus Ponens

In propositional logic and several other logics, Modus Ponens is a rule of inference. It states that if we derived a well formed formula $\phi \to \psi$ and we also derived $\phi$, then we may derive $\psi$ (where $\phi$ and $\psi$ are metavariables and $\to$ is Material Conditional). In sequent notation, it is:

$\phi \to \psi ,\phi \vdash \psi$ 

In rule form it is:

${\frac {P\to Q,P}{\therefore Q}}$

It is also the valid argument form:

1. If P then Q.

2. P.

C: Q.