theorem Th32:
  A1 \+\ B1 = { x1 : not x1 in A1 iff x1 in B1 }
proof
A1: for x1 holds (x1 in A1 & not x1 in B1 or not x1 in A1 & x1 in B1) iff (
  not x1 in A1 iff x1 in B1);
  defpred Q[set] means not $1 in A1 iff $1 in B1;
  defpred P[set] means $1 in A1 & not $1 in B1 or not $1 in A1 & $1 in B1;
A2: A1 \+\ B1 = { x1 : x1 in A1 & not x1 in B1 or not x1 in A1 & x1 in B1 }
  by Th31;
  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;
