Yuri Balashov, PHIL 2500 Lecture Notes Derivations in Predicate Logic The Natural Deduction System PD Derivation rules of PD = Derivation rules of SD (applied to complete sentences of PL considered as wholes) + New rules for introduction and elimination of quantifiers (“intelim” rules for (∀x) and (∃x)) Derive: (∃x) Ux 1⏐(∀x) Hx ⊃(∃y) Uy Assum. 2 ⏐(∃x) (∀y) (Sx ∨Pxy) & (∀x) Hx Assum. ⏐————————————— 3 ⏐(∀x) Hx 2 &E4 ⏐(∃x) Ux 1,3 ⊃E1
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