Constructive Dilemma/Formulation 1/Proof 3

Theorem

$p \implies q, r \implies s \vdash p \lor r \implies q \lor s$

Proof

By the tableau method of natural deduction:

$p \implies q, r \implies s \vdash p \lor r \implies q \lor s$

Line		Pool	Formula	Rule	Depends upon	Notes
1		1	$p \implies q$	Premise	(None)
2		2	$r \implies s$	Premise	(None)
3		1	$p \lor r \implies q \lor r$	Sequent Introduction	1	Factor Principles/Disjunction on Right/Formulation 1/Proof 2
4		1	$q \lor r \implies q \lor s$	Sequent Introduction	2	Factor Principles/Disjunction on Left/Formulation 1/Proof 2
5		1	$p \lor r \implies q \lor s$	Sequent Introduction	3,4	Hypothetical Syllogism

$\blacksquare$