In page 157 of Di Francesco (Conformal Field Theory) it is said that the holomorphic and antiholomorphic components of the energy-momentum tensor have the trivial OPE
$T(z) \bar{T}(\bar{w}) \sim 0$.
I don't know if this was explained earlier in the book and I missed it or it is trivial and I don't see it. Do you have a proof?
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