Rule of Idempotence/Conjunction/Formulation 1/Forward Implication
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Theorem
- $p \vdash p \land p$
Proof
By the tableau method of natural deduction:
Line | Pool | Formula | Rule | Depends upon | Notes | |
---|---|---|---|---|---|---|
1 | 1 | $p$ | Premise | (None) | ||
2 | 1 | $p \land q$ | Rule of Conjunction: $\land \II$ | 1, 1 |
$\blacksquare$