Extension by new constant and function names

In mathematical logic, conservativity theorem states the following: Suppose that $\exists x_{1}\ldots \exists x_{n}\,\varphi (x_{1},\ldots ,x_{n})$ is a theorem of a first-order theory $T$. Let $T_{1}$ be a theory obtained from $T$ by extending its language with new constants $a_{1},\ldots ,a_{n}$ and adding new axiom $\varphi (a_{1},\ldots ,a_{n})$. Then $T_{1}$ is a conservative extension of $T$, which means that the theory $T_{1}$ has the same set of theorems in the original language as the theory $T$.