Does the following equivalence
$$\lnot \lnot (A \lor B) \leftrightarrow (\lnot \lnot A \lor \lnot \lnot B)$$
hold in propositional intuitionistic logic? And in propositional minimal logic? (In propositional classical logic this is obvious since $A \leftrightarrow \lnot\lnot A$ is classically provable.)
Actually I have a proof that $(\lnot \lnot A \lor \lnot \lnot B) \to \lnot \lnot (A \lor B)$ holds in propositional minimal logic, so I'm interested in the converse implication:
$$\lnot \lnot (A \lor B) \to (\lnot \lnot A \lor \lnot \lnot B)$$
If it is minimally or/and intuitionistically provable, I would like a (reference to a) direct proof in natural deduction-style.