Rule of Idempotence/Disjunction/Formulation 1/Forward Implication
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Theorem
- $p \vdash p \lor p$
Proof
By the tableau method of natural deduction:
| Line | Pool | Formula | Rule | Depends upon | Notes | |
|---|---|---|---|---|---|---|
| 1 | 1 | $p$ | Premise | (None) | ||
| 2 | 1 | $p \lor p$ | Rule of Addition: $\lor \II_1$ | 1 |
$\blacksquare$
Sources
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $5$ Further Proofs: Résumé of Rules: Theorem $33 \ \text{(a)}$