Simplification

For the practice of "simplifying" fractions, see Fraction (mathematics)#Equivalent fractions.

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.

$A \and B \vdash A$

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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