theorem Th5:
  (for p holds p in W1 iff p in W2) implies W1 = W2
proof
  assume
A1: for p holds p in W1 iff p in W2;
  thus W1 c= W2
  proof
    let x be object;
    assume x in W1;
    then reconsider p = x as Element of W1;
 p in W2 by A1;
    hence thesis;
  end;
  let x be object;
  assume x in W2;
  then reconsider p = x as Element of W2;
 p in W1 by A1;
  hence thesis;
end;
