
theorem lemNor1cu:
for F being Field,
    E1 being FieldExtension of F
for E2 being Field st E1 == E2 holds E2 is FieldExtension of F
proof
let F be Field, E1 be FieldExtension of F, E2 be Field;
assume E1 == E2; then
A: E1 is Subfield of E2 by FIELD_7:def 2;
F is Subfield of E1 by FIELD_4:7;
then F is Subfield of E2 by A,EC_PF_1:5;
hence thesis by FIELD_4:7;
end;
