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 conditional implies the_antecedent_of (H/(x,y)) = (
the_antecedent_of H)/(x,y) & the_consequent_of (H/(x,y)) = (the_consequent_of H
  )/(x,y)
proof
  assume
A1: H is conditional;
  then H/(x,y) is conditional by Th175;
  then
A2: H/(x,y) = (the_antecedent_of (H/(x,y))) => (the_consequent_of (H/(x,y)))
  by ZF_LANG:47;
  H = (the_antecedent_of H) => (the_consequent_of H) by A1,ZF_LANG:47;
  hence thesis by A2,Th162;
end;
