∀ {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A] [inst_2 : Module R A]
  [inst_3 : SMulCommClass R A A] [inst_4 : IsScalarTower R A A] {C : Type u_5} [inst_5 : Semiring C]
  [inst_6 : Algebra R C] {φ ψ : Unitization R A →ₐ[R] C},
  φ = ψ ↔ (↑φ).comp (Unitization.inrNonUnitalAlgHom R A) = (↑ψ).comp (Unitization.inrNonUnitalAlgHom R A)