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We introduce a calculus for transforming first-order proofs of theorems originally formulated in modal logic, into modal natural deduction proofs. With a transformation procedure based on this calculus, we are able to present a proof in the language in which the problem was originally formulated, and in a formalism giving better insight into the contents of the proof. As a target language of the proof transformation we use a linearized modal natural deduction calculus which makes the reasoningdoi:10.1093/logcom/10.4.527 fatcat:65uxc5ornbfslocepkn4mcpztq