Separation property for the calculus E

Let $\mathbf{E}$ be the calculus introduced in the paper, and call a formula derivable in $\mathbf{E}$ when it has a derivation in that calculus. The calculus uses axioms grouped as $(\mathbf{i})$ and $(\mathbf{c})$–$(\mathbf{m})$, with the latter groups corresponding to logical connectives.

Separation property for $\mathbf{E}$. Any formula derivable in $\mathbf{E}$ is also derivable using only the axioms in group $(\mathbf{i})$ and those groups among $(\mathbf{c})$–$(\mathbf{m})$ corresponding to the logical connectives actually appearing in the formula.

The separation property is a structural property of the calculus asserting that irrelevant connective-specific axioms can be omitted. The surrounding discussion indicates that this property is being investigated for $\mathbf{E}$ and that the paper will show that the separation property for the minimal modalized Heyting calculus does not hold; the status of this assertion itself is not established by the supplied excerpt.