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;
