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Firstly, the disjunctive elimination rule is proved valid in Esteva and Godo's MTL and Hájek's BL logics. Secondly, from this rule a general method is presented for finitely axiomatizing the intersection of the sets of theorems of two given schematic extensions of MTL or BL. Thirdly, the axiomatic system of NM is simplified by replacing the axiom schemata (NM) with another which is built up with one...
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