Clavius's Law

Theorem
Consequentia Mirabilis (also known as Clavius's Law) is a particular case of reduction ad absurdum.

It states that:
 * If, from the negation of a proposition $$\,\!p$$ we can derive $$\,\!p$$, we can conclude $$\,\!p$$.

In symbolic form:


 * $$\neg p \implies p \vdash p$$
 * $$\vdash (\neg p\implies p)\implies p$$

Proof
Proof using natural deduction:

Source of name
The name Consequentia Mirabilis is Latin for "marvellous (or admirable) consequence".

The name Clavius's Law (or Clavius' Law) is for Christopher Clavius.