reserve p,p1,p2,q,r,F,G,G1,G2,H,H1,H2 for ZF-formula,
  x,x1,x2,y,y1,y2,z,z1,z2,s,t for Variable,
  a,X for set;

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;
