Disjunction elimination

In propositional logic disjunction elimination is the inference that, if "A or B" is true, and A entails C, and B entails C, then we may justifiably infer C. The reasoning is simple: since at least one of the statements A and B is true, and since either of them would be sufficient to entail C, C is certainly true.

For example:
 * It is true that either I'm inside or I'm outside. It is also true that if I'm inside, I have my wallet on me.  It's also true that if I'm outside, I have my wallet on me.  Given these three premises, it follows that I have my wallet on me.

Formally:

( A ∨ B ) ( A → C ) ( B → C ) ∴ C