Proof by Contradiction/Variant 3/Formulation 2/Proof 1

Theorem

$\vdash \paren {p \implies \neg p} \implies \neg p$

Proof

By the tableau method of natural deduction:

$\vdash \paren {p \implies \neg p} \implies \neg p$

Line		Pool	Formula	Rule	Depends upon	Notes
1		1	$p \implies \neg p$	Assumption	(None)
2		1	$\neg p$	Sequent Introduction	1	Proof by Contradiction: Variant 3: Formulation 1
3			$\paren {p \implies \neg p} \implies \neg p$	Rule of Implication: $\implies \II$	1 – 2	Assumption 1 has been discharged

$\blacksquare$