How do I correctly sub-license a library that is under the MIT license?

Question

How do I correctly sub-license a library that is under the MIT license.

I am using and extending the library. The MIT license states that I am free to sub-license the library.

Can I simply state:

<Software library> is copyright <original author> and licensed under the MIT license.

<orignal license>

Extensions to <Software library> are copyright <me> and licensed under the GPL license, 
or commercial license if applicable.

<GPL, or commercial license>