In propositional logic, simplification (equivalent to conjunction elimination) 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 can be expressed in formal language as:
where the rule is that whenever instances of "" appear on lines of a proof, either "" or "" can be placed on a subsequent line by itself.
The simplification rule may be written in sequent notation:
where and are propositions expressed in some logical system.