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Full Idea
The Cut rule (from A|-B and B|-C, infer A|-C) directly expresses the classical doctrine that entailment is transitive.
Gist of Idea
The Cut Rule expresses the classical idea that entailment is transitive
Source
John P. Burgess (Philosophical Logic [2009], 5.3)
Book Ref
Burgess,John P.: 'Philosophical Logic' [Princeton 2009], p.106