Double Negation/Double Negation Introduction/Sequent Form/Formulation 1

Theorem

$p \vdash \neg \neg p$

Proof

By the tableau method of natural deduction:

$p \vdash \neg \neg p$

Line		Pool	Formula	Rule	Depends upon	Notes
1		1	$p$	Premise	(None)
2		2	$\neg p$	Assumption	(None)
3		1, 2	$\bot$	Principle of Non-Contradiction: $\neg \EE$	1, 2
4		1	$\neg \neg p$	Proof by Contradiction: $\neg \II$	2 – 3	Assumption 2 has been discharged

$\blacksquare$