I read in my lecture notes that if $\Sigma\_1$, $\Sigma\_2$ are theories in the same Language such that $\Sigma\_1 \subset \Sigma\_2$ and $\Sigma\_1$ is Henkin then also $\Sigma\_2$ is Henkin.

Unfortunately there is no proof and I don't have any idea how to show this, because it seems to be not true to me. However, since this result will be used later I guess it is true.