Principle of Non-Contradiction/Proof Rule

Theorem
The Principle of Non-Contradiction is a valid deduction sequent in propositional logic.

As a proof rule it is expressed in the form:
 * If we can conclude both $\phi$ and $\neg \phi$, we may infer a contradiction.

It can be written:
 * $\displaystyle {\phi \quad \neg \phi \over \bot} \neg_e$