theorem
  the_left_side_of (p <=> q) = p & the_right_side_of (p <=> q) = q
proof
  p <=> q is biconditional;
  then
  p <=> q = (the_left_side_of (p <=> q)) <=> (the_right_side_of (p <=> q))
  by ZF_LANG:49;
  hence thesis by ZF_LANG:33;
end;
