reserve Omega for set;
reserve X, Y, Z, p,x,y,z for set;
reserve D, E for Subset of Omega;
reserve f for Function;
reserve m,n for Nat;
reserve r,r1 for Real;
reserve seq for Real_Sequence;
reserve F for Field_Subset of X;

theorem
  { {}, X } is Field_Subset of X
proof
  {} c= X & X in bool X by ZFMISC_1:def 1;
  then reconsider EX = { {}, X } as Subset-Family of X by Th2;
  now
    let A be Subset of X;
A1: A = {} implies A` = X;
    A = X implies A` = {} X by XBOOLE_1:37;
    hence A in EX implies A` in EX by A1,TARSKI:def 2;
  end;
  hence thesis by Def1;
end;
