Save "Liked From Radio" to my library

[w5sv52m_-a1s]

I've got a bunch of songs in the playlist "Liked from Radio," but none of these songs show up in my LIbrary (i.e. they don't appear in Songs).  Is this the expected behavior?  

How can I quickly add all the songs in my "Liked from Radio" playlist to my library?  I'm a big fan of hitting shuffle on all my songs, but nothing from Radio is included.