Rule of Simplification/Sequent Form/Formulation 2/Proof 1/Form 2
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Theorem
- $\vdash p \land q \implies q$
Proof
By the tableau method of natural deduction:
Line | Pool | Formula | Rule | Depends upon | Notes | |
---|---|---|---|---|---|---|
1 | 1 | $p \land q$ | Assumption | (None) | ||
2 | 1 | $q$ | Rule of Simplification: $\land \EE_2$ | 1 | ||
3 | $p \land q \implies q$ | Rule of Implication: $\implies \II$ | 1 – 2 | Assumption 1 has been discharged |
$\blacksquare$