In propositional logic, disjunction elimination (sometimes named proof by cases, case analysis, or or elimination) is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof. It is the inference has to be true. The reasoning is simple: since at least one of the statements P and R is true, and since either of them would be sufficient to entail Q, Q is certainly true.

An example in English:

1. 1. If I'm inside, I have my wallet on me.

2. 2. If I'm outside, I have my wallet on me.

3. 3. It is true that either I'm inside or I'm outside.

4. Therefore, I have my wallet on me.

It is the rule can be stated as:

" can be placed on a subsequent line.

Formal notation

The disjunction elimination rule may be written in sequent notation:

is a metalogical is a syntactic consequence in some logical system;

and expressed as a truth-functional tautology or theorem of propositional logic:

are propositions expressed in some formal system.

See also

• Disjunction

• Argument in the alternative

• Disjunct normal form

• Proof by exhaustion

References