reserve F,H,H9 for ZF-formula,
  x,y,z,t for Variable,
  a,b,c,d,A,X for set;
reserve E for non empty set,
  f,g,h for Function of VAR,E,
  v1,v2,v3,v4,v5,u5 for Element of VAL E;

theorem
  H is conjunctive implies for f holds f in St(the_left_argument_of H,E)
  & f in St(the_right_argument_of H,E) iff f in St(H,E)
proof
  assume H is conjunctive;
  then H = (the_left_argument_of H) '&' the_right_argument_of H by ZF_LANG:40;
  hence thesis by Th5;
end;
