# 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: