now :: thesis: for n being Element of NAT st 1 < n & n * n <= 23 & n is prime holds
not n divides 23

let n be Element of NAT ; :: thesis: ( 1 < n & n * n <= 23 & n is prime implies not n divides 23 )
23 = (2 * 11) + 1 ;
then A1: not 2 divides 23 by Th9;
23 = (3 * 7) + 2 ;
then A2: not 3 divides 23 by Th9;
assume ( 1 < n & n * n <= 23 & n is prime ) ; :: thesis: not n divides 23
hence not n divides 23 by A1, A2, Lm3; :: thesis: verum

end;

hence 23 is prime by Th14; :: thesis: verum