Before I could demo the rest of the floor I needed to remove the old vanity.  I was hoping to get it off in one piece, however this proved to difficult and I ended up breaking it apart to get rid of it.   After carefully undoing all of the plumbing connections on the sink, I lifted the sink up.  To my surprise, the drain did not come apart at the spot where I had undone it, but had instead just ripped in two at the trap.  After taking a moment to be impressed with my own strength, I realized that the walls on the drain pipe were incredibly thin, and I was once again happy that we had decided to get rid of it, as it seemed like just a matter of time before it failed.  Another interesting note is that this appears to not have been the original sink, as it looks like there are holes in the tile to support a pedestal sink.