The aim of this paper is to show that the principles of logics based on the Law of Contradiction are not universal in the sense that their use can appear to be irrelevant if premises are contradictory.

The aim of this paper is to present a modified version of the notion of strong proof from hypotheses (definition D2), and to give three deduction theorems for the relevant logicsR (theoremsT1, andT2) andE (theoremT3).