Universal property of de Rham differential.
You can describe the universal property of all of the de Rham differentials at once as follows. The direct sum $\Omega(A) = \bigoplus_i \Omega^i(A)$ together with the differential has the structure of a graded-commutative dg-algebra. There is a forgetful functor from graded-commutative dg-algebras to commutative algebras sending a dg-algebra to its degree-$0$ subalgebra, and the functor $A \mapsto \Omega(A)$ is its left adjoint.