Let $\phi$ be a Boolean formula and $\mathrm{Tseitin}(\phi)$ the corresponding Tseitin transformed equisatifiable formula.
It is well-known that one can get a variable assignment for $\phi$ by solving $\mathrm{Tseitin}(\phi)$ and dropping the auxiliary variables. For example, see Wiki, quote: "When a satisfying assignment of variables is found, those assignments for the introduced variables can simply be discarded."
After a long search through SAT papers I just could not find any paper which proves this statement. Because I do not want to re-invent the wheel: Does anyone know such a reference I can use to cite?