
theorem thisofield:
for F being Field,
    Z being set
ex E being Field st E,F are_isomorphic &
                    (the carrier of E) /\ ((the carrier of F) \/ Z) = {}
proof
let F be Field, Z be set;
set r = the Renaming of (the carrier of F),Z;
take E = RenField r;
r" is linear by thiso; then
r" is isomorphism by thiso,MOD_4:def 12;
hence E,F are_isomorphic;
rng r = the carrier of E by defrf;
hence thesis by defr;
end;
