  Spin density matrices of the system, containing arbitrary even number N of
indistinguishable fermions with spin S = 1/2, described by antisymmetric wave
function, have been calculated. The indistinguishability and the Pauli
principles are proved to determine uniquely spin states, spin correlations and
entanglement of fermion spin states. Increase of the particle number in the
multifermion system reduces the spin correlation in any pair of fermions. The
fully entangled system of N electrons are shown to be composed by pairs with
nonentangled spin states that is the incoherent superposition of the singlet
and triplet states. Any large system of N fermions, such as electrons with spin
S = 1/2, the spin state of any particle are shown to be entangled with the
other part of the system containing N-1 particle. However, the spin state of
this electron is not entangled with any other particle, and spin state of any
electron pair is not entangled. These properties of spin states manifest in the
Einstein-Podolsky-Rosen as confirmation or violation of the Bell inequalities
indicating the presence of non-local quantum spin correlations.
