We prove that a commutative (resp. modified anticommutative) connected graded Hopf algebra over a commutative algebra over a field of characteristic zero is a symmetric algebra (resp. exterior algebra) if and only if it satisfies a certain “condistributive law”, expressed by a commutative diagram. Both results are obtained as a corollary of an analogous characterization of the symmetric superalgebra of a supermodule over a superring: The symmetric superalgebras over a superringRin characteristic zero are exactly the comodules over the symmetric superalgebra ofR