Proof by Contradiction/Sequent Form
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Theorem
The Proof by Contradiction can be symbolised by the sequent:
- $\paren {p \vdash \bot} \vdash \neg p$
Proof
By the tableau method of natural deduction:
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: $\neg \II$ | 2 – 2 | Assumption 2 has been discharged |
$\blacksquare$