 This is really a whole range of examples. As we required (∨E) for Example 1, here we require (→I). Let us call a consequence relation ⊢ →-introductive if Γ, φ ⊢ ψ always implies Γ ⊢ φ →  ψ.[39]  Now suppose ⊢ ⊇ ⊢I L and ⊢ is →-introductive, and either (i) for some n-ary connective #, ⊢ satisfies the conditions induced (on consequence relations) by the determinant ⟨F,…, F,T⟩ (n occurrences of “F”) for #, as well as some determinant with F as its final entry, or (ii) ⊢ satisfies the conditions induced by the determinant ⟨T,…,T, F⟩ (n occurrences of “T”) as well as some determinant with T as final entry (for n-ary #). Then it follows that ⊢ ⊇ ⊢CL.