  To conclude, we give a simple application of this theorem. Let A = ⟨A, ∈ ⨡ A⟩ be a model of ZFC. A model B = ⟨B, E⟩ of ZFC is said to be a proper end-extension of A if (i) A ⊆ B, (ii) A ≠ B, (iii) a ∈ A, b ∈ B, bEa ⇒ b∈A. Thus a proper end-extension of a model of ZFC is a proper extension in which no “new” element comes “before” any “old” element. As our application of 5.5 we prove 