
theorem Th21:
  for C1,C2 being non empty AltGraph, o2 being Object of C2 st <^o2,o2^> <> {}
  for m be Morphism of o2,o2, o1 being Object of C1 holds (C1 --> m).o1 = o2
proof
  let C1,C2 be non empty AltGraph, o2 be Object of C2 such that
A1: <^o2,o2^> <> {};
  let m be Morphism of o2,o2, o1 be Object of C1;
A2: [o1,o1] in [:the carrier of C1,the carrier of C1:] by ZFMISC_1:87;
  thus (C1 --> m).o1 =
  (([:the carrier of C1,the carrier of C1:] --> [o2,o2]).(o1,o1))`1
  by A1,Def17
    .= [o2,o2]`1 by A2,FUNCOP_1:7
    .= o2;
end;
