The inference rule for deductive systems $\text{L}$ (or sometimes a theory in one) in which $\supset$ represents the material conditional licensing the inference

That is, for all $\text{L}$-theorems of the form $\phi \supset \psi$, the material conditional is detachable. Because the material conditional is definable from negation $\neg$ and disjunction $\vee$, rule $\gamma$ may equivalently be stated as a form of disjunctive syllogism for theorems, i.e., as the rule

When considering the status of $\gamma$ in theories, the rule sometimes appears in a different form, i.e., as the inference

In this form, for a theory $T$, it is said that $T$ admits rule $\gamma$ if $T{⊢}_{\text{L}}\psi$ whenever $T{⊢}_{\text{L}}\phi \supset \psi$ and $T{⊢}_{\text{L}}\psi$, i.e., $T$ is closed under modus ponens for the material conditional. It is possible that a logic $\text{L}$ admits $\gamma$ on theorems while there exist $\text{L}$-theories that do not admit $\gamma$.