reserve x, X, Y for set;

theorem
  for L, M being non empty RelStr for f being Function of L, M for y
  being Element of Image f ex x being Element of L st f.x = y
proof
  let L1, L2 be non empty RelStr, g be Function of L1,L2;
  let s be Element of Image g;
  dom g = the carrier of L1 by FUNCT_2:def 1;
  then
A1: rng g is non empty by RELAT_1:42;
  rng g = the carrier of Image g by YELLOW_0:def 15;
  then consider l being object such that
A2: l in dom g and
A3: s = g.l by A1,FUNCT_1:def 3;
  reconsider l as Element of L1 by A2;
  take l;
  thus thesis by A3;
end;
