reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;
reserve F,G for Cardinal-Function;
reserve A,B for set;

theorem Th72:
  for X be with_common_domain functional set st X = {{}} holds DOM X = {}
proof
  let X be with_common_domain functional set;
  assume
A1: X = {{}};
  {} in {{}} by TARSKI:def 1;
  hence thesis by A1,Lm2,RELAT_1:38;
end;
