reserve x, x1, x2, y, z, X9 for set,
  X, Y for finite set,
  n, k, m for Nat,
  f for Function;
reserve F,Ch for Function;

theorem Th33:
 for y being object holds
  Ch"{y}={} implies Intersection(F,Ch,y)=union rng F
proof let y be object;
  reconsider E ={} as set;
A1: Ch|E={} & Intersection(F,{},y)=union rng F by Th25;
  assume Ch"{y}={};
  then (Ch|E)"{y} = Ch"{y};
  hence thesis by A1,Th32;
end;
