Rule of Idempotence/Disjunction/Formulation 2/Reverse Implication
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Theorem
- $\vdash \left({p \lor p}\right) \implies p$
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 | |
4 | $\left({p \lor p}\right) \implies p$ | Rule of Implication: $\implies \II$ | 1 – 3 | Assumption 1 has been discharged |
$\blacksquare$
Also see
- This is an axiom of the following proof system: