∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {D : Type u₂} {inst_1 : CategoryTheory.Category.{v₂, u₂} D}
  {F : CategoryTheory.Functor C D} {preimage : {X Y : C} → (F.obj X ⟶ F.obj Y) → (X ⟶ Y)}
  {map_preimage :
    autoParam (∀ {X Y : C} (f : F.obj X ⟶ F.obj Y), F.map (preimage f) = f)
      CategoryTheory.Functor.FullyFaithful.map_preimage._autoParam}
  {preimage_map :
    autoParam (∀ {X Y : C} (f : X ⟶ Y), preimage (F.map f) = f)
      CategoryTheory.Functor.FullyFaithful.preimage_map._autoParam}
  {preimage_1 : {X Y : C} → (F.obj X ⟶ F.obj Y) → (X ⟶ Y)}
  {map_preimage_1 :
    autoParam (∀ {X Y : C} (f : F.obj X ⟶ F.obj Y), F.map (preimage_1 f) = f)
      CategoryTheory.Functor.FullyFaithful.map_preimage._autoParam}
  {preimage_map_1 :
    autoParam (∀ {X Y : C} (f : X ⟶ Y), preimage_1 (F.map f) = f)
      CategoryTheory.Functor.FullyFaithful.preimage_map._autoParam},
  { preimage := preimage, map_preimage := map_preimage, preimage_map := preimage_map } =
      { preimage := preimage_1, map_preimage := map_preimage_1, preimage_map := preimage_map_1 } →
    preimage = preimage_1