# Law of Excluded Middle/Explanation

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## Proof Rule

The **law of (the) excluded middle** can be expressed in natural language as:

This is one of the Aristotelian principles upon which rests the whole of classical logic, and the majority of mainstream mathematics.

The **LEM** is rejected by the intuitionistic school, which rejects the existence of an object unless it can be constructed within an axiomatic framework which does not include the LEM.