∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] {φ₁ φ₂ : A →ₐ[R] B}, φ₁ = φ₂ ↔ ∀ (x : A), φ₁ x = φ₂ x