In propositional calculus 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
