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
  H is biconditional implies the_right_side_of H = the_consequent_of
  the_left_argument_of H & the_right_side_of H = the_antecedent_of
  the_right_argument_of H
proof
  assume H is biconditional;
  then H = (the_left_side_of H) <=> (the_right_side_of H) by ZF_LANG:49;
  then
  the_left_argument_of H = (the_left_side_of H) => (the_right_side_of H )
  & the_right_argument_of H = (the_right_side_of H) => (the_left_side_of H) by
Th4;
  hence thesis by Th6;
end;
