Proof by Contradiction/Sequent Form

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Theorem

The Proof by Contradiction can be symbolised by the sequent:

$\left({p \vdash \bot}\right) \vdash \neg p$


Proof

By the tableau method of natural deduction:

$\left({p \vdash \bot}\right) \vdash \neg p$
Line Pool Formula Rule Depends upon Notes
1 1 $p \vdash \bot$ Premise (None)
2 2 $p$ Assumption (None)
3 1 $\neg p$ Proof by Contradiction: $\neg \mathcal I$ 2 – 2 Assumption 2 has been discharged


$\blacksquare$