  We consider the system of 3 nonrelativistic spinless fermions in two
dimensions, which interact through spherically-symmetric pair interactions.
Recently a claim has been made for the existence of the so-called super Efimov
effect [Y. Nishida et al., Phys. Rev. Lett. 110, 235301 (2013)]. Namely, if the
interactions in the system are fine-tuned to a p-wave resonance, an infinite
number of bound states appears, whose negative energies are scaled according to
the double exponential law. We present the mathematical proof that such system
indeed has an infinite number of bound levels. We also prove that $\lim_{E \to
0} |\ln|\ln E||^{-1} N(E) = 8/(3\pi) $, where $N(E)$ is the number of bound
states with the energy less than $-E <0$. The value of this limit is equal
exactly to the value derived in [Y. Nishida et al.] using renormalization group
approach. Our proof resolves a recent controversy about the validity of results
in [Y. Nishida et al.].
