reserve A,B,C for Category,
  F,F1,F2,F3 for Functor of A,B,
  G for Functor of B, C;
reserve m,o for set;

theorem
  for a,b being Object of A st Hom(a,b) <> {} for f being Morphism of a,
  b holds (id A)/.f = f
proof
  let a,b be Object of A such that
A1: Hom(a,b) <> {};
  let f be Morphism of a,b;
  thus (id A)/.f = (id A).(f qua Morphism of A) by A1,CAT_3:def 10
    .= f by FUNCT_1:18;
end;
