Rule of Idempotence/Disjunction/Formulation 1/Reverse Implication
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Theorem
- $p \lor p \vdash p$
Proof
By the tableau method of natural deduction:
Line | Pool | Formula | Rule | Depends upon | Notes | |
---|---|---|---|---|---|---|
1 | 1 | $p \lor p$ | Premise | (None) | ||
2 | 2 | $p$ | Assumption | (None) | ||
3 | 1 | $p$ | Proof by Cases: $\text{PBC}$ | 1, 2 – 2, 2 – 2 | Assumptions 2 and 2 have been discharged |
$\blacksquare$
Sources
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $5$ Further Proofs: Résumé of Rules: Theorem $33 \ \text{(b)}$