Principle of Non-Contradiction

Context
The rule of not-elimination is one of the axioms of natural deduction.

The rule
If we can conclude both $$p$$ and $$\neg p$$, we may infer a contradiction:


 * $$p, \neg p \vdash \bot$$


 * Abbreviation: $$\neg \mathcal{E}$$
 * Deduced from: The pooled assumptions of $$p$$ and $$\neg p$$.
 * Depends on: The lines containing $$p$$ and $$\neg p$$.

Explanation
This means: if we have managed to deduce that a statement is both true and false, then the sequence of deductions show that the pool of assumptions upon which the sequent rests contains assumptions which are mutually contradictory.

Thus it provides a means of eliminating a logical not from a sequent.