Notice the additional node in this diagram, DET . In this case, it is nothing more than the article required by the English language to modify certain nouns in certain contexts. Teachers are professionals. To dance is to live.
Dancing bears become overnight stars by strutting their stuff in public.
We need not go into much detail on this sentence pattern. While the adjectival subject complement modifies the subject, we might say that the nominal subject complement renames the subject. Note the examples. The second example gives us a different slant. Here we have infinitive phrases serving both as subject and subject complement.