  System I is a proof language for a fragment of propositional logic where
isomorphic propositions, such as $A\wedge B$ and $B\wedge A$, or
$A\Rightarrow(B\wedge C)$ and $(A\Rightarrow B)\wedge(A\Rightarrow C)$ are made
equal. System I enjoys the strong normalization property. This is sufficient to
prove the existence of empty types, but not to prove the introduction property
(every closed term in normal form is an introduction). Moreover, a severe
restriction had to be made on the types of the variables in order to obtain the
existence of empty types. We show here that adding $\eta$-expansion rules to
System I permits to drop this restriction, and yields a strongly normalizing
calculus which enjoys the full introduction property.
