reserve N,M,K for ExtNat;
reserve X for ext-natural-membered set;

theorem
  (for N holds N in X) implies X = ExtNAT
proof
  assume A1: for N holds N in X;
  A2: X c= ExtNAT by ThSubset;
  for x being object st x in ExtNAT holds x in X by A1;
  then ExtNAT c= X by TARSKI:def 3;
  hence thesis by A2, XBOOLE_0:def 10;
end;
