I don't actually use either of these verbs and am quite unfamiliar with "predicate of." However:
"predicate on" means something like "is dependent on" or "is based on"
(I just found the following in a letter to the New York Times: "We predicate our actions on our beliefs...")
(my dictionary tells me) "predicate of" means some thing like "ascribe to" or "describe as having [some characteristic]." (I think it's quite an uncommon usage and would probably be regarded as pedantic in many contexts.)
Incidentally, I think both of the verbs you mention are ditransitive prepositional, verbs (not phrasal).
Student or Learner