reserve B,C,D,C9,D9 for Category;
reserve E for Subcategory of C;

theorem
  for c being Object of C, d being Object of D holds (Obj pr1(C,D)).(c,d ) = c
proof
  let c be Object of C, d be Object of D;
  id [c,d] = [id c,id d] & (pr1(C,D)).(id c,id d) = id c by Th25,FUNCT_3:def 4;
  hence thesis by CAT_1:67;
end;
