Principle of Non-Contradiction

Context
This is one of the axioms of natural deduction.

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

$$p, \lnot p \vdash \bot$$

This is sometimes known as:


 * "implies-introduction";
 * "conditional proof" (abbreviated CP).


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

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.