theorem
for F being Field,
    R being Subring of F holds R is Subfield of F iff R is Field
proof
let F be Field, R be Subring of F;
the carrier of R c= the carrier of F
  & the addF of R = (the addF of F)||the carrier of R
  & the multF of R = (the multF of F)||the carrier of R
  & 1.R = 1.F & 0.R = 0.F by C0SP1:def 3;
hence thesis by EC_PF_1:def 1;
end;
