Proof by Contradiction/Proof Rule

Proof Rule
Proof by Contradiction is a valid deduction sequent in propositional logic.

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 does not depend upon the assumption $\phi$.

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