 We can take the intuitionistic (and classical) rules to differ from these in replacing the formula variable χ with a set-of-formulas variable Γ. The latter set is stronger in the sense that there are sequents provable with its rules (e.g., p, q ≻ p ∧ q) which are not provable on the basis of the displayed rules (together with the standard structural rules, if desired). But clearly the displayed rules uniquely characterize ∧, since, once we reduplicate them for ∧′, we can take χ in the second and third (collectively, (∧E)-style) rules to be φ ∧ ψ, to derive both φ ∧ ψ ≻ φ and φ ∧ ψ ≻ ψ, from which by the reduplicated version of the first (“(∧′I)”) rule we derive φ ∧ ψ ≻ φ ∧′ ψ—with a similar derivation for the converse sequent.