reserve C for Category,
  C1,C2 for Subcategory of C;

theorem Th24:
  for C being Category, a being Object of C, f being Morphism of C holds
  f in a Hom iff dom f = a
proof
  let C be Category, a be Object of C, f be Morphism of C;
  dom f in {a} iff dom f = a by TARSKI:def 1;
  hence thesis by FUNCT_2:38;
end;
