
theorem Th16:
  for C being non empty category, f1,f2 being morphism of C st
  MORPHISM(f1) = MORPHISM(f2) holds f1 = f2
  proof
    let C be non empty category;
    let f1,f2 be morphism of C;
    assume
A1: MORPHISM(f1) = MORPHISM(f2);
    consider f be morphism of OrdC 2 such that
A2: f is not identity &
    Ob OrdC 2 = {dom f, cod f} & Mor OrdC 2 = {dom f, cod f, f} &
    dom f, cod f, f are_mutually_distinct by CAT_7:39;
    thus f1 = (MORPHISM f1).f by A2,CAT_7:def 16
    .= f2 by A1,A2,CAT_7:def 16;
  end;
