
theorem Th34:
  for C being para-functional category
  for a,b being Object of C st <^a,b^> <> {} for f being Morphism of a,b
  holds f is Function of the_carrier_of a, the_carrier_of b
proof
  let C be para-functional category;
  let a,b be Object of C such that
A1: <^a,b^> <> {};
  let f be Morphism of a,b;
A2: <^a,b^> c= Funcs(the_carrier_of a, the_carrier_of b) by Th33;
  f in <^a,b^> by A1;
  hence thesis by A2,FUNCT_2:66;
end;
