Constructive Dilemma/Formulation 2

Theorem

$\ds \paren {p \implies q} \land \paren {r \implies s}$

$\ds $

$\ds p \lor r$

$\ds $

$\ds \vdash \ \ $

$\ds q \lor s$

$\ds $

$\paren {p \implies q} \land \paren {r \implies s}, p \lor r \vdash q \lor s$
Line	Pool	Formula	Rule	Depends upon	Notes
1	1	$\paren {p \implies q} \land \paren {r \implies s}$	Premise	(None)
2	2	$p \lor r$	Premise	(None)
3	1, 2	$\paren {p \lor r} \land \paren {p \implies q} \land \paren {r \implies s}$	Rule of Conjunction: $\land \II$	2, 1	Associativity is implicit
4		$\paren {\paren {p \lor r} \land \paren {p \implies q} \land \paren {r \implies s} } \implies \paren {q \lor s}$	Theorem Introduction	(None)	Constructive Dilemma: Formulation 3
5	1, 2	$q \lor s$	Modus Ponendo Ponens: $\implies \mathcal E$	4, 3

$\blacksquare$

1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.3$: Argument Forms and Truth Tables: Exercise $\text{I} \ \mathbf k.$
1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $3$: The Method of Deduction: $3.1$: Formal Proof of Validity: Rules of Inference: $5.$
1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{II}$: The Logic of Statements $(2): \ 1$: Decision procedures and proofs: $3$