Does P not NP imply NP COMPLETE disjoint from RP?

According to Wikipedia https://en.wikipedia.org/wiki/RP_(complexity), $ P \ne NP$ implies that $ RP$ is a strict subset of $ NP$ . Does anybody have a reference? Furthermore, am I correct that if this indeed the case, then $ NP-COMPLETE \cap RP = \emptyset$ since we can use $ NP$ completeness to solve all other $ NP$ problems?