Using statements and reading files

Question

I have code that contained two using statements. The Inner using statement is reading a response stream and the outer is opening a file to write the response too.

The following code works fine (sfd is a SaveFileDialog):

using (Stream fs = sfd.OpenFile())
using (var responseStream = response.GetResponseStream())
{
    // Work
}

The following does not work

using (Stream fs = sfd.OpenFile())
{
    using (var responseStream = response.GetResponseStream())
    {
        // Work
    }
}

The only difference is that I inputted the curly braces to make the code more readable, but that breaks the code. Any ideas as to why? It does not quite make sense yet.