
theorem pr1:
for E being Field, F being Subfield of E holds F is Subring of E
proof
let E be Field, F be Subfield of E;
the carrier of F c= the carrier of E
  & the addF of F = (the addF of E) || the carrier of F
  & the multF of F = (the multF of E) || the carrier of F
  & 1.E = 1.F & 0.E = 0.F by EC_PF_1:def 1;
hence thesis by C0SP1:def 3;
end;
