  Within a programme of developing a general schema for rules for arbitrary logical constants, Schroeder-Heister (1984) proposed that a logically complex formula should express the content or common content of systems of rules. This means that not the introduction rules are considered basic but the consequences of defining conditions. A rule R is either a formula A or has the form R1,…,Rn ⇒ A, where R1,…,Rn are themselves rules. These so-called “higher-level rules” generalize the idea that rules may discharge assumptions to the case where these assumptions can themselves be rules. For the standard logical constants this means that A∧B expresses the content of the pair (A,B); A → B expresses the content of the rule A ⇒ B; A∨B expresses the common content of A and B; and absurdity ⊥ expresses the common content of the empty family of rule systems. In the case of arbitrary n-ary propositional connectives this leads to a natural deduction system with generalized introduction and elimination rules. These general connectives are shown to be definable in terms of the standard ones, establishing the expressive completeness of the standard intuitionistic connectives.