Double Negation/Double Negation Elimination/Sequent Form/Formulation 1/Proof

Theorem

 * $\neg \neg p \vdash p$

Proof

 * align="right" | 2 ||
 * align="right" | (None)
 * $p \lor \neg p$
 * LEM
 * (None)
 * (None)


 * align="right" | 5 ||
 * align="right" | 1, 4
 * $\bot$
 * $\neg \mathcal E$
 * 4, 1
 * align="right" | 6 ||
 * align="right" | 1, 4
 * $p$
 * $\bot \mathcal E$
 * 5
 * align="right" | 7 ||
 * align="right" | 1
 * $p$
 * $\lor \mathcal E$
 * 2, 3-3, 4-6
 * }
 * align="right" | 1
 * $p$
 * $\lor \mathcal E$
 * 2, 3-3, 4-6
 * }
 * }

Also see

 * Double Negation Elimination implies Law of Excluded Middle