Consequentia mirabilis
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Consequentia mirabilis (Admirable consequence), also known as Clavius's Law, is used in classical logic to establish the truth of a proposition from the inconsistency of its negation. It is thus similar to reductio ad absurdum, but it can prove a proposition true using just its negation. It states that if a proposition is a consequence of its negation, then it is true, for consistency. It can thus be demonstrated without using any other principle, but that of consistency.
In formal notation: 
