Geodesic
The theory of Zermelo-Fraenkel sets with Hilbert $\varepsilon$-terms
Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 569-575.

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In this paper we study the role of functioning axioms on the deductive power of the system obtained from the Zermelo–Fraenkel $\mathrm{ZF}$ system by the introduction of $\varepsilon$-terms with the possibility of using them as a scheme for the substitution axiom. It is proved that if the system has a founding axiom the introduction of $\varepsilon$-terms does not extend the class of $\mathrm{ZF}$ theorems, while if the founding axiom is absent, there is an extension of the $\mathrm{ZF}$ theorems. 
@article{MZM_1972_12_5_a9,
     author = {V. N. Grishin},
     title = {The theory of {Zermelo-Fraenkel} sets with {Hilbert} $\varepsilon$-terms},
     journal = {Matemati\v{c}eskie zametki},
     pages = {569--575},
     publisher = {mathdoc},
     volume = {12},
     number = {5},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a9/}
}
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V. N. Grishin. The theory of Zermelo-Fraenkel sets with Hilbert $\varepsilon$-terms. Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 569-575. http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a9/