reserve Y for non empty set,
  G for Subset of PARTITIONS(Y),
  A,B,C,D,E,F for a_partition of Y;

theorem
  for B,C,D,b,c,d being object st B<>C & D<>B holds
    ((B,C,D) --> (b,c,d)).B = b by FUNCT_4:134;
