Clavius's Law/Formulation 2

Theorem
If, from the negation of a proposition $p,$ we can derive $p$, we can conclude $p$:
 * $\vdash \left({\neg p \implies p}\right) \implies p$

This result is known as Clavius's law.

Proof

 * align="right" | 2 ||
 * align="right" | 1
 * $p$
 * SI
 * 1
 * using Formulation 1 of this law
 * align="right" | 3 ||
 * align="right" |
 * $\left({\neg p \implies p}\right) \implies p$
 * $\implies \mathcal I$
 * 1, 2
 * Assumption 1 has been discharged
 * 1, 2
 * Assumption 1 has been discharged