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

theorem
  for f,g being Function, x,y,z being set st dom f = dom g & f.x = g.x &
  f.y = g.y & f.z = g.z holds f|{x,y,z} = g|{x,y,z}
proof
  let f,g be Function, x,y,z be set;
  assume dom f = dom g & f.x = g.x & f.y = g.y & f.z = g.z;
  then
A1: f|{x,y} = g|{x,y} & f|{z} = g|{z} by Th27,Th28;
  {x,y,z} = {x,y} \/ {z} by ENUMSET1:3;
  hence thesis by A1,RELAT_1:150;
end;
