∀ {f : ZFSet.{u_1} → ZFSet.{u_1}} {x z : ZFSet.{u_1}} (y : ZFSet.{u_1})
  (motive : (∃ z_1 ∈ x, z_1.pair (f z_1) = z.pair y) → Prop) (x_1 : ∃ z_1 ∈ x, z_1.pair (f z_1) = z.pair y),
  (∀ (w : ZFSet.{u_1}) (left : w ∈ x) (we : w.pair (f w) = z.pair y), motive ⋯) → motive x_1