Proof
(related to Corollary: Reduction of $\epsilon$NFA to DFA)
 First, reduce a given $\epsilon$NFA to an NFA according to theorem about the reduction of epsilonnfa to nfa.
 Now, reduce the resulting NFA to a DFA according to the RabinScott theorem.
 This shows the set inclusion $\mathcal L(\epsilon\operatorname{NFA})\subseteq\mathcal L(\operatorname{DFA}).$
 The other set inclusion $\mathcal L(\operatorname{DFA})\subseteq\mathcal L(\epsilon\operatorname{NFA})$ is trivial.
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References
Bibliography
 Erk, Katrin; Priese, Lutz: "Theoretische Informatik", Springer Verlag, 2000, 2nd Edition
 Hoffmann, Dirk: "Theoretische Informatik, 3. Auflage", Hanser, 2015