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:


 * $$\neg p \implies p \vdash p$$

It can alternatively be rendered as:


 * $$\vdash \left({\neg p \implies p}\right) \implies p$$

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.