
theorem Th30:
  for A being non empty AltGraph, o1,o2 being Object of A st <^o1,o2^> <> {}
  for m being Morphism of o1,o2 holds Morph-Map(id A,o1,o2).m = m
proof
  let A be non empty AltGraph, o1,o2 be Object of A such that
 <^o1,o2^> <> {};
  let m be Morphism of o1,o2;
A1: [o1,o2] in [:the carrier of A, the carrier of A:] by ZFMISC_1:87;
  Morph-Map(id A,o1,o2) = (id the Arrows of A).[o1,o2] by Def29;
  hence Morph-Map(id A,o1,o2).m
  = (id((the Arrows of A).(o1,o2))).m by A1,MSUALG_3:def 1
    .= (id<^o1,o2^>).m by ALTCAT_1:def 1
    .= m;
end;
