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:

1. It's raining and it's pouring.

2. Therefore it's raining.

The rule consists of two separate sub-rules, which can be expressed in formal language as:

and

" can be placed on a subsequent line by itself. The above example in English is an application of the first sub-rule.

Formal notation

The conjunction elimination sub-rules may be written in sequent notation:

and

is a metalogical is a syntactic consequence in logical system;

and expressed as truth-functional tautologies or theorems of propositional logic:

and

are propositions expressed in some formal system.

References

sv:Matematiskt uttryck#Förenkling