reserve E,X,Y,x for set;
reserve A,B,C for Subset of E;
reserve x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 for Element of X;

theorem
  X <> {} implies {x1,x2,x3} is Subset of X
proof
  set A = {x1,x2,x3};
  assume
A1: X <> {};
  then
A2: x3 in X by Def1;
  x1 in X & x2 in X by A1,Def1;
  then A c= X by A2,ENUMSET1:def 1;
  then A in bool X by ZFMISC_1:def 1;
  hence thesis by Def1;
end;
