  We establish the non-perturbative validity of the gauge anomaly cancellation
condition in an effective electroweak theory of massless fermions with finite
momentum cut-off and Fermi interaction. The requirement that the current is
conserved up to terms smaller than the energy divided by the cut-off scale,
which is the natural condition as gauge invariance is only emerging, produces
the same constraint on charges as in the Standard Model. The result holds at a
non-perturbative level as the functional integrals are expressed by convergent
power series expansions and are analytic in a finite domain.
