Law of Excluded Middle/Proof Rule

Proof Rule
The law of (the) excluded middle is a valid argument in certain types of logic dealing with disjunction $\lor$ and negation $\neg$.

This includes classical propositional logic and predicate logic, and in particular natural deduction, but for example not intuitionistic propositional logic.

As a proof rule it is expressed in the form:
 * $\phi \lor \neg \phi$ for all statements $\phi$.

It can be written:
 * $\ds {{} \over \phi \lor \neg \phi} \textrm{LEM} \qquad \text { or } \qquad {\top \over \phi \lor \neg \phi} \textrm{LEM}$

where the symbol $\top$ (top) signifies tautology.

Also see

 * This is a rule of inference of the following proof systems:
 * Definition:Natural Deduction