Reductio ad Absurdum/Variant 1/Proof by Truth Table

Theorem

$\neg p \implies \bot \vdash p$

Proof

As can be seen by inspection, the truth values under the main connectives match for all boolean interpretations.

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

$\blacksquare$