 The Causal Markov Condition implies the generalized version of RCCP presented in  Section 2.  This is most easily seen using the d-separation version. If variables X and Y are correlated, then \(\{X\}\) and \(\{Y\}\) are not d-separated by the empty set. This means that at least one path between X and Y must be without a collider. If we further assume that neither variable is a cause of the other, then there is no directed path between them. It then follows that the collider-free path must contain a common cause: a variable Z that has both X and Y as descendants. Furthermore, the set of all such common causes d-separates \(\{X\}\) and \(\{Y\}\). (The proof is a bit fussy, since a common cause on one path can be a collider on another path.) Hence the set of common causes of X and Y will screen them off from one another.