"Define a coproduct  \Delta : L \rightarrow L \otimes L by \Delta(x) = x \otimes 1 + 1 \otimes x , for some  x \in L

Show that \Delta defined above is a universal enveloping algebra homomorphism."

Do I simply take  x,y \in L, and prove that  \Delta(xy) = \Delta(x)\Delta(y) ??