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
  A1 \+\ B1 = { x1 : x1 in A1 iff not x1 in B1 }
proof
A1: for x1 holds (not x1 in A1 iff x1 in B1) iff (x1 in A1 iff not x1 in B1);
  defpred Q[set] means $1 in A1 iff not $1 in B1;
  defpred P[set] means not $1 in A1 iff $1 in B1;
A2: A1 \+\ B1 = { x1 : not x1 in A1 iff x1 in B1 } by Th32;
  for X1 st for x1 holds P[x1] iff Q[x1] holds { y1 : P[y1] } = { z1 : Q[
  z1] } from Fraenkel6;
  hence thesis by A1,A2;
end;
