10.1 - Yuri Balashov PHIL 2500 Lecture Notes Derivations in...

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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 &E 4 ( x) Ux 1,3 E 1
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