In http://arxiv.org/abs/hep-th/9108028 Equation (2.22), the correlation function of then energy-momentum tensor with some primary fields is
We can view this as sum over the OPE of the energy-momentum tensor with each of the primary fields. I don't quite understand why we need to sum over the OPE of $T(z)$ with all the primaries. Usually when we say that we can use the OPE to reduce a n-point function to $n-1$ point functions, I think we just need to use the OPE of T(z) with $\phi_1$ in the above equations. What I am asking is why the LHS in the above equation is equal to sum of terms for $j$ from 1 to n , instead of just the term $j=1$?