  A non perturbative proof of the mass generation of fermions via the Higgs
mechanism is given. This is done by showing exponential decay of the two point
fermionic correlation function in a weakly coupled U(1) Higgs-Yukawa theory on
a unit lattice in $d=4$. This decay implies that the Higgs boson, the photon
and the fermion all have a non zero physical mass and the theory is said to
have a mass gap.
