**Consequentia Mirabilis**, also known as Clavius’ Law (after the German mathematician) is the principal in classical logic

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That is, it’s the principle that if a proposition’s negation implies the proposition, then the proposition must be true.

Its use is similar in form to that *reductio ad absurdum*. To use *reductio ad absurdum*, one assumes that a proposition is false, sees that a contradiction follows, and from this concludes that the proposition must be true. To use *consequentia mirabilis*, by contrast, one assumes that a proposition is false, sees that the proposition itself follows, and from this concludes that the proposition must be true.

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