Derivability of admissible rules

A rule is admissilbe (conservative) if every deduction of its premises can be transformed into a deduction of the conclusion. A rule is (directly) derivable if there exists a derivation of its conclusion from the premises. It is known [2] that there exists a rule closed under substitution and admissible but underivable in the intuitionistic propositional caloulus (IPC). The main result: any admissible (in IPC) rule of the form $A_1,\dots,A_n\vdash A$ is derivable provided that at least one of the connectives $\supset,V$ does not occur in it. The result is the best possible as is shown by the rule (I).