Tautology is Negation of Contradiction/Proof by Truth Table

Theorem
A tautology implies and is implied by the negation of a contradiction:


 * $\top \dashv \vdash \neg \bot$

That is, a truth can not be false, and a non-falsehood must be a truth.

Proof
We apply the Method of Truth Tables to the proposition.

As can be seen by inspection, the truth values in the appropriate columns match.

$\begin{array}{|c||cc|} \hline \bot & \neg & \top \\ \hline F & F & T \\ \hline \end{array}$