Geodesic
The theory of Zermelo-Fraenkel sets with Hilbert $\varepsilon$-terms
Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 569-575 
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/
@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},
     year = {1972},
     volume = {12},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.