now :: thesis: not 2 divides 3

3 = (2 * 1) + 1 ;
hence not 2 divides 3 by NAT_4:9; :: thesis: verum

end;

then for n being Element of NAT st 1 < n & n * n <= 3 & n is prime holds
not n divides 3 by XPRIMET1:2;
hence 3 is prime by NAT_4:14; :: thesis: verum