This well-known usage of "down with" appears in Webster's New World College Dictionary, curiously flush with exclamation points:
down with! overthrow! do away with!
Yet the online version of the American Heritage Dictionary also lists that other, hipper version of "down with":
Slang. Having knowledge of; aware; "He was not, I detected, 'down with the revolution'" (Clarence Page).
And urbandictionary.com reports the next phase of this term's evolution:
down wit dat: to be in agreement
And here we have yet another example of why native English speakers should go easy on anyone trying to learn this language: The protesters who were originally "down with!" sexism changed their minds and instead became "down with" sexism.