Rule of Addition/Sequent Form/Formulation 2/Form 2
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Theorem
- $\vdash q \implies \left({p \lor q}\right)$
Proof
By the tableau method of natural deduction:
Line | Pool | Formula | Rule | Depends upon | Notes | |
---|---|---|---|---|---|---|
1 | 1 | $q$ | Premise | (None) | ||
2 | 1 | $p \lor q$ | Rule of Addition: $\lor \II_2$ | 1 | ||
3 | $q \implies \paren {p \lor q}$ | Rule of Implication: $\implies \II$ | 1 – 3 | Assumption 1 has been discharged |
$\blacksquare$
Also see
- This is an axiom of the following proof system: