
theorem
for F being Field
for E being FieldExtension of F
for A being AlgebraicClosure of F
st A is E-extending holds A is AlgebraicClosure of E
proof
let F be Field, E be FieldExtension of F;
let A be AlgebraicClosure of F;
assume A is E-extending; then
reconsider B = A as FieldExtension of E;
B is E-algebraic by FIELD_7:40;
hence thesis by defAC;
end;
