If R is a univalent, then R;R^T is transitive.
: proof: Suppose Then there are a and b such that Since R is univalent, yRb and aR^Ty imply a=b. Therefore xRaR^Tz, hence xR;R^Tz and R;R^T is transitive.

Corollary: If R is univalent, then R;R^T is an equivalence relation on the domain of R.
: proof: R;R^T is symmetric and reflexive on its domain. With univalence