
theorem FA2:
for p being Prime
for n being non zero Nat
for F being Field st card F = p|^n holds card(PrimeField F) = p
proof
let p be Prime, n be non zero Nat, F be Field;
assume AS: card F = p|^n;
set P = PrimeField F;
Char F = p by AS,T5; then
P,Z/p are_isomorphic by RING_3:114; then
consider f being Function of P,Z/p such that E: f is one-to-one onto;
card dom f = card(Z/p) by E,CARD_1:70 .= p by fresh3a;
hence thesis by FUNCT_2:def 1;
end;
