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=== Formal proofs === {{Main|Formal proof}} A ''formal proof'' is a sequence of well-formed formulas of a formal language, the last of which is a [[theorem]] of a formal system. The theorem is a [[Logical consequence|syntactic consequence]] of all the well formed formulae that precede it in the proof system. For a well formed formula to qualify as part of a proof, it must result from applying a rule of the deductive apparatus of some formal system to the previous well formed formulae in the proof sequence.
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