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.

Comment
Note that the proof of:
 * $\neg \bot \vdash \top$

relies indirectly, via Reductio Ad Absurdum, upon Law of Excluded Middle, and it can be seen that this is just another way of stating that truth.

The proposition:
 * If it's not false, it must be true

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

From the intuitionistic perspective, this result does not hold.