Principle of Non-Contradiction/Explanation
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Theorem
The Principle of Non-Contradiction can be expressed in natural language as follows:
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.
It is one of the cornerstones of Aristotelian logic, along with the law of the excluded middle.