Homologie of Lie algebra with coefficients in tensor product of modules

Question

I'd like to prove that $H_i(\mathfrak g, M\otimes N)=\operatorname{Tor}_i^{U \mathfrak g}(M,N).$ My idea was that $H_i(\mathfrak g, M\otimes N)=\operatorname{Tor}_i^{U \mathfrak g}(k,M\otimes N)$. Both $\operatorname{Tor}_i^{U \mathfrak g}(k,M\otimes N)$ and $\operatorname{Tor}_i^{U \mathfrak g}(M,N)$ are universal $\delta-$functors in both arguments and $\operatorname{Tor}_0^{U \mathfrak g}(k,M\otimes N)=\operatorname{Tor}_0^{U \mathfrak g}(M,N),$ so they are isomorphic for any $i$. But i can't understand why is $\operatorname{Tor}_0^{U \mathfrak g}(k,-\otimes N)$ is an universal $\delta-$functor?