Relevant implication and the weak deduction theorem

Studia Logica 46 (3):239 - 245 (1987)
It is shown that the implicational fragment of Anderson and Belnap's R, i.e. Church's weak implicational calculus, is not uniquely characterized by MP (modus ponens), US (uniform substitution), and WDT (Church's weak deduction theorem). It is also shown that no unique logic is characterized by these, but that the addition of further rules results in the implicational fragment of R. A similar result for E is mentioned
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DOI 10.1007/BF00372548
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M. Richard Diaz (1981). Topics in the Logic of Relevance. Monograph Collection (Matt - Pseudo).

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