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 disjunctive implies the_left_argument_of (H/(x,y)) = (
  the_left_argument_of H)/(x,y) & the_right_argument_of (H/(x,y)) = (
  the_right_argument_of H)/(x,y)
proof
  assume
A1: H is disjunctive;
  then H/(x,y) is disjunctive by Th174;
  then
A2: H/(x,y) = (the_left_argument_of (H/(x,y))) 'or' (the_right_argument_of (
  H/(x,y))) by ZF_LANG:41;
  H = (the_left_argument_of H) 'or' (the_right_argument_of H) by A1,ZF_LANG:41;
  hence thesis by A2,Th161;
end;
