reserve X,Y for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,h for Function;

theorem Th28:
  for f,g being Function, x,y being set st dom f = dom g & f.x = g
  .x & f.y = g.y holds f|{x,y} = g|{x,y}
proof
  let f,g be Function, x,y be set;
  assume dom f = dom g & f.x = g.x & f.y = g.y;
  then
A1: f|{x} = g|{x} & f|{y} = g|{y} by Th27;
  {x,y} = {x} \/ {y} by ENUMSET1:1;
  hence thesis by A1,RELAT_1:150;
end;
