Rule of Addition/Sequent Form/Formulation 2/Form 2

Theorem

$\vdash q \implies \left({p \lor q}\right)$

Proof

By the tableau method of natural deduction:

$q \implies \paren {p \lor q}$
Line Pool Formula Rule Depends upon Notes
1 1 $q$ Premise (None)
2 1 $p \lor q$ Rule of Addition: $\lor \mathcal I_2$ 1
3 $q \implies \paren {p \lor q}$ Rule of Implication: $\implies \mathcal I$ 1 – 3 Assumption 1 has been discharged

$\blacksquare$