 The axioms (MTL4a)–(MTL4c) replace the axiom of "divisibility" (BL4) of BL.The axioms (MTL5a) and (MTL5b) express the law of residuation and the axiom (MTL6) corresponds to the condition of prelinearity.The axioms (MTL2) and (MTL3) of the original axiomatic system were shown to be redundant (Chvalovský, 2012) and (Cintula, 2005).