Double Negation Elimination implies Law of Excluded Middle

Theorem
Let the Law of Double Negation Elimination be supposed to hold:
 * $\neg \neg p \vdash p$

Then the Law of the Excluded Middle likewise holds:
 * $\vdash p \lor \neg p$

Proof
By the tableau method of natural deduction:

Comment
Thus the Law of Double Negation Elimination may be taken as an axiom instead of the Law of the Excluded Middle.