Some detail here. What goes on in relational algebra is that the FROMCLAUSE is encoded into an axiomatic primitive called a RELATION and you get stuff like this:
SELECTCLAUSE(WHERECLAUSE(relation)) = relation
WHERECLAUSE(SELECTCLAUSE(relation)) = relation
Basically every operation in relational algebra produces a primitive of type RELATION which allows for all operations to be composed like unix pipes.
My example in the previous post has a flaw where it's not clear what:
SELECTCLAUSE * WHERECLAUSE = ????
will output because there's no meaning to a SQLEXPRESSION without a FROMCLAUSE. But hopefully it illustrates the point. I'm putting this here for anyone who's nitpicky about the details. The relational algebra syntax is much more elegant.