reserve A,B,C for Category,
  F,F1,F2,F3 for Functor of A,B,
  G for Functor of B, C;
reserve m,o for set;
reserve t for natural_transformation of F,F1,
  t1 for natural_transformation of F1,F2;

theorem Th29:
  for f being Morphism of Functors(A,B) st f = [[F,F1],t] holds
  dom f = F & cod f = F1
proof
  let f be Morphism of Functors(A,B) such that
A1: f = [[F,F1],t];
  thus dom f = f`1`1 by Def16
    .= [F,F1]`1 by A1
    .= F;
  thus cod f = f`1`2 by Def16
    .= [F,F1]`2 by A1
    .= F1;
end;
