reserve a,b,c,d for set,
  D,X1,X2,X3,X4 for non empty set,
  x1,y1,z1 for Element of X1,
  x2 for Element of X2,
  x3 for Element of X3,
  x4 for Element of X4,
  A1,B1 for Subset of X1;
reserve x,y for Element of [:X1,X2,X3:];
reserve x for Element of [:X1,X2,X3,X4:];
reserve A2 for Subset of X2,
  A3 for Subset of X3,
  A4 for Subset of X4;

theorem
  X1 = the set of all x1
proof
  defpred P[set] means not contradiction;
A1: y1 in the set of all  x1 ;
  { x1 : P[x1] } is Subset of X1 from SubsetD;
  hence thesis by A1,SUBSET_1:28;
end;
