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A deduction from a set is a sequence of well-formed formulas with each element being justified as a tautology or the result of a rule of inference. A deduction from the empty set is a proof.

Formal definitionEdit

Let \mathcal{S} be a formal system and let \mathcal{L} be it's underlying formal language and let \Delta \subseteq \mathcal{L}

Then a deduction of S_n from \Deltais a sequence S_1,\ldots,S_n of well-formed formulas such that one of the following holds for 1\leq i \leq n:

  1. \vdash S_i
  2. S_i \in \Delta
  3. S_i is justified by a rule of inference of \mathcal{S}.

A deduction of S_n from \Delta is a proof if and only if \Delta = \emptyset.

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