Prove a language is not recursive enumerable I need to prove 
$: L=\left\{&lt;M&gt;| M \text { is a } T M \text { and } L(M)=L\left((01)^{*}\right)\right\} \notin R e$

at first observation it looks like it's immediate from Rice's extended Thm, but is it really?
Rice's extended Thm requires that the set won't include sigma star and won't be empty, as I believe $L\left((01)^{*}\right)$ meets the conditions? or do I have to make some manipulation in order to meet the requirements of the Thm.
Yes it's okay to use Rice's extended theorem.

To clarify, the theorem states: "if $C$ is some set of languages, and $C\neq\emptyset\wedge\Sigma^*\notin C$, then $\{&lt;M&gt;|L(M)\in C\}\notin RE$."

So, let us define $C=\{L((01)^*)\}$. Notice that our $L$ in the question is exaclty $\{&lt;M&gt;|L(M)\in C\}$, and then since $C\neq\emptyset$ and $\Sigma^*\notin C$ $[$as the only language in $C$ is $L((01)^*)\space]$, we have by the extended theorem that $L\notin RE$.