A Nonstandard Delta Function in a Predicative Theory

In [1] Todorov has shown by means of axiomatic set theory that there exists a nonstandard function Δ: *?ⁿ → * ? such that for all continuous functions φ: ?ⁿ → ?, . Here *? and *? are the set of the nonstandard real numbers and the set of the nonstandard complex numbers, respectively, and *φ: *?ⁿ → *? is the nonstandard extension of φ In the present note we want to prove an analogous theorem by predicative means only.