Tautology and Contradiction

Comment
Note that the proofs of:


 * $\neg \bot \vdash \top$
 * $\neg \top \vdash \bot$
 * $p \vdash p \land \top$
 * $p \lor \top \vdash \top$

rely (directly or indirectly) upon Law of Excluded Middle - and it can be seen that they are just another way of stating that truth.

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

and
 * If it's not true, it must be false

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

From the intuitionistic perspective, these results do not hold.