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;
reserve M for non empty set,
  m,m9 for Element of M,
  v,v9 for Function of VAR,M;
reserve i,j for Element of NAT;

theorem
  H is biconditional implies the_left_side_of (H/(x,y)) = (
the_left_side_of H)/(x,y) & the_right_side_of (H/(x,y)) = (the_right_side_of H)
  /(x,y)
proof
  assume H is biconditional;
  then H = (the_left_side_of H) <=> (the_right_side_of H) & H/(x,y) = (
  the_left_side_of (H/(x,y))) <=> (the_right_side_of (H/(x,y))) by Th176,
ZF_LANG:49;
  hence thesis by Th163;
end;
