Reductio ad Absurdum/Variant 1/Proof 1

Theorem

 * $\neg p \implies \bot \vdash p$

Proof

 * align="right" | 3 ||
 * align="right" | 1, 2
 * $\bot$
 * $\bot \mathcal E$
 * 1, 2
 * align="right" | 4 ||
 * align="right" | 1
 * $\neg \neg p$
 * Proof by Contradiction
 * 2-3
 * align="right" | 5 ||
 * align="right" | 1
 * $p$
 * $\neg \neg \mathcal E$
 * 4
 * }
 * align="right" | 1
 * $p$
 * $\neg \neg \mathcal E$
 * 4
 * }
 * }