
theorem lift9:
for F1,F2 being Field,
    E being FieldExtension of F1 st F1 == F2 holds E is FieldExtension of F2
proof
let F1,F2 be Field, E be FieldExtension of F1;
assume F1 == F2; then
A: F2 is Subfield of F1 by FIELD_7:def 2;
   F1 is Subfield of E by FIELD_4:7; then
   F2 is Subfield of E by A,EC_PF_1:5;
hence thesis by FIELD_4:7;
end;
