reserve C for category,
  o1, o2, o3 for Object of C;

theorem Th51:
  for o1, o2 being Object of AllEpi C for m being Morphism of o1,
  o2 st <^o1,o2^> <> {} holds m is epi
proof
  let o1, o2 be Object of AllEpi C, m be Morphism of o1, o2 such that
A1: <^o1,o2^> <> {};
  reconsider p1 = o1, p2 = o2 as Object of C by Def2;
  reconsider p = m as Morphism of p1, p2 by A1,ALTCAT_2:33;
  p is epi by A1,Def2;
  hence thesis by A1,Th37;
end;
