
theorem XX:
for F being Field
for E being F-algebraic FieldExtension of F
ex A being AlgebraicClosure of F st E is Subfield of A
proof
let F be Field, E be F-algebraic FieldExtension of F;
set K = the AlgebraicClosure of E;
reconsider K as FieldExtension of F;
reconsider K as E-extending FieldExtension of F;
K is F-algebraic by FIELD_7:39; then
reconsider K as AlgebraicClosure of F by defAC;
take K;
thus thesis by FIELD_4:7;
end;
