Rule of Explosion/Proof Rule

Proof Rule
The rule of explosion is a valid argument in certain types of logic dealing with contradiction $\bot$.

This includes classical propositional logic and predicate logic, and in particular natural deduction, but for example not Johansson's minimal logic.

As a proof rule it is expressed in the form:
 * If a contradiction can be concluded, it is possible to infer any statement $\phi$.

It can be written:
 * $\ds {\bot \over \phi} \bot_e$

Also see

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