Disjunction with Tautology/Proof 1

Theorem

 * $p \lor \top \dashv \vdash \top$

Proof

 * align="right" | 5 ||
 * align="right" | 3
 * $\top$
 * LEM
 * 4
 * 4

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.