theorem Th91:
for F,K being Field holds
K = PrimeField F iff (K is strict Subfield of F &
                      for E being strict Subfield of K holds E = K)
proof
let F,K be Field;
now assume A1: K is strict Subfield of F &
              for E being strict Subfield of K holds E = K;
   then PrimeField F is Subfield of K by Th90;
   hence K = PrimeField F by A1;
   end;
hence thesis by Th89;
end;
