
theorem mmk:
for F being Field
for E being FieldExtension of F,
    K being F-extending FieldExtension of E
for a being F-algebraic Element of E,
    b being F-algebraic Element of K st b = a holds FAdj(F,{a}) = FAdj(F,{b})
proof
let F be Field;
let E be FieldExtension of F, K be F-extending FieldExtension of E;
let a be F-algebraic Element of E, b be F-algebraic Element of K;
assume AS: b = a;
E is Subfield of K by FIELD_4:7;
then FAdj(F,{a}) is Subfield of K by EC_PF_1:5;
hence thesis by AS,bba,EC_PF_1:8;
end;
