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

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


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