reserve k,m,n for Element of NAT,
  a,X,Y for set,
  D,D1,D2 for non empty set;
reserve p,q for FinSequence of NAT;
reserve x,y,z,t for Variable;
reserve F,F1,G,G1,H,H1 for ZF-formula;
reserve sq,sq9 for FinSequence;

theorem
  H is biconditional implies (F = the_left_side_of H iff ex G st H = F
  <=> G) & (F = the_right_side_of H iff ex G st H = G <=> F) by Def37,Def38;
