Disjunction elimination

Disjunction elimination is the inference that, if A or B is true, and both A and B entail C, then we may justifiably infer C.

For example, it's true that either I'm inside or I'm outside. It's 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