Simplification (logic)

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In mathematical logic, simplification is a valid simple argument of the form:

A and B, therefore A

or

A and B, therefore B

or in logical operator notation:

<math> A \and B \vdash A </math>

or

<math> A \and B \vdash B </math>

The argument has one premise, namely a conjunction, and one often uses simplification in longer arguments to make one of the conjuncts available. As a strategy it is fairly straightforward, so much so, it may have been overlooked in the past. Since A and B implies B and A, one form of the argument can be used to derive the other. An example in English:

It's raining and it's pouring.

Therefore it's raining.