theorem Th55:
for F being Field, E being F-homomorphic Field, K being Subfield of F
for f being Function of F,E, g being Function of K,E st
g = f|(the carrier of K) & f is unity-preserving
holds g is unity-preserving
proof
let F be Field,
    E be F-homomorphic Field,
    K be Subfield of F,
    f be Function of F,E,
    g be Function of K,E such that
A1: g = f|(the carrier of K) and
A2:  f is unity-preserving;
  thus g.(1_K) = f.(1_K) by A1,FUNCT_1:49
  .= 1_E by A2,EC_PF_1:def 1;
end;
