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: $\lor \II_2$	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:
  • Definition:Hilbert Proof System/Instance 2