It is known that RP is a subset of BPP, and BPP is a subset of PP. It is not known whether those two are strict subsets, since we don't even know if P is a strict subset of PSPACE. BPP is contained in the second level of the polynomial hierarchy and therefore it is contained in PH. More precisely, the Sipser–Lautemann theorem states that formula_1. As a result, P = NP leads to P = BPP since PH collapses to P in this case. Thus either P = BPP or P ≠ NP or both.