Consequentia mirabilis

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: $$ (\neg A \rightarrow A) \rightarrow A $$

The most famous example is René Descartes's "cogito ergo sum": If nothing exists, at least this thought exists, thus the thinker. Even if I can question the existence of the thinker, I can't doubt the thought.