Proof by Contradiction/Proof Rule

Proof Rule
Proof by contradiction is a valid argument in types of logic dealing with negation $\neg$ and contradiction $\bot$.

This includes classical propositional logic and predicate logic, and in particular natural deduction.

As a proof rule it is expressed in the form:
 * If, by making an assumption $\phi$, we can infer a contradiction as a consequence, then we may infer $\neg \phi$.


 * The conclusion $\neg \phi$ does not depend upon the assumption $\phi$.

It can be written:
 * $\ds {\begin{array}{|c|} \hline \phi \\ \vdots \\ \bot \\ \hline \end{array} \over \neg \phi} \ \textrm{PBC}$

Also see

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