# Clavius's Law/Formulation 2/Proof by Truth Table

## Theorem

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

## Proof

We apply the Method of Truth Tables.

As can be seen by inspection, the truth value under the main connective is true for all boolean interpretations.

$\begin{array}{|cccc|c|c|} \hline (\neg & p & \implies & p) & \implies & p \\ \hline \T & \F & \F & \F & \T & \F \\ \F & \T & \T & \T & \T & \T \\ \hline \end{array}$

$\blacksquare$

## Source of Name

This entry was named for Christopher Clavius.