reserve p,q,x,x1,x2,y,y1,y2,z,z1,z2 for set;
reserve A,B,V,X,X1,X2,Y,Y1,Y2,Z for set;
reserve C,C1,C2,D,D1,D2 for non empty set;

theorem Th7:
  for f being Function st X in dom(.:f) holds (.:f).X = f.:X
proof
  let f be Function;
  assume X in dom(.:f);
  then X in bool dom f by Def1;
  hence thesis by Def1;
end;
