Principle of Non-Contradiction/Proof Rule

Theorem
The principle of non-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 we can conclude both $\phi$ and $\neg \phi$, we may infer a contradiction.

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