We prove path-wise uniqueness for an abstract stochastic reaction-diffusion equation in Banach spaces. The drift contains a bounded H{o}lder term; in spite of this, due to the space-time white noise it is possible to prove path-wise uniqueness. The proof is based on a detailed analysis of the associated Kolmogorov equation. The model includes examples not covered by the previous works based on Hilbert spaces or concrete SPDEs. Joint work with G. Da Prato and F. Flandoli.