
theorem
for F being Field
for E being F-algebraic FieldExtension of F
for A being AlgebraicClosure of E holds A is AlgebraicClosure of F
proof
let F be Field, E be F-algebraic FieldExtension of F;
let A be AlgebraicClosure of E;
reconsider B = A as FieldExtension of F;
B is F-algebraic by FIELD_7:39;
hence thesis by defAC;
end;
