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In mathematical logic, simplification (equivalent to conjunction elimination) is a valid argument 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.

In formal language:

 A \and B \vdash A

or

 A \and B \vdash B

The argument has one premise, namely a conjunction, and one often uses simplification in longer arguments to derive one of the conjuncts.

An example in English:

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

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