Factor Principles/Disjunction on Right/Formulation 1/Proof 1

Theorem

$p \implies q \vdash \paren {p \lor r} \implies \paren {q \lor r}$

Proof

By the tableau method of natural deduction:

$p \implies q \vdash \paren {p \lor r} \implies \paren {q \lor r} $

Line		Pool	Formula	Rule	Depends upon	Notes
1		1	$p \implies q$	Premise	(None)
2			$r \implies r$	Theorem Introduction	(None)	Law of Identity: Formulation 2
3		1	$\paren {p \lor r} \implies \paren {q \lor r}$	Sequent Introduction	1, 2	Constructive Dilemma

$\blacksquare$