Tautology is Negation of Contradiction

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 by Boolean Interpretation
That is, the proposition:
 * If it's not false, it must be true

is valid only in the context where there are only two truth values.

Also see

 * Contradiction is Negation of Tautology