reserve o,m for set;
reserve C for Cartesian_category;
reserve a,b,c,d,e,s for Object of C;

theorem
  (id a)[x](id b) = id(a[x]b)
proof
  Hom(a[x]b,b) <> {} by Th19;
  then
A1: (id b)*pr2(a,b) = pr2(a,b) by CAT_1:28;
  Hom(a[x]b,a) <> {} by Th19;
  then (id a)*pr1(a,b) = pr1(a,b) by CAT_1:28;
  hence thesis by A1,Th24;
end;
