Theorems in propositional logic | Rules of inference

Conjunction elimination

In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, or simplification) is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true. The rule makes it possible to shorten longer proofs by deriving one of the conjuncts of a conjunction on a line by itself. An example in English: It's raining and it's pouring.Therefore it's raining. The rule consists of two separate sub-rules, which can be expressed in formal language as: and The two sub-rules together mean that, whenever an instance of "" appears on a line of a proof, either "" or "" can be placed on a subsequent line by itself. The above example in English is an application of the first sub-rule. (Wikipedia).

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Related pages

Tautology (logic) | Propositional calculus | Logical consequence | Metalogic | Rule of inference | Formal system | Inference | Immediate inference | Logical conjunction | Formal language | Validity (logic) | Sequent | Formal proof