What is the law of disjunction elimination?

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What is the law of disjunction elimination?

The law of disjunction elimination, also known as the rule of proof by cases, states that if we have a disjunction (A or B) and we can prove a statement C from both A and B separately, then we can conclude C. In other words, if we have evidence that either A or B is true, and we can show that C follows from both A and B, then we can infer that C is true.