given a, b, c being Prime such that a,b,c are_mutually_distinct and
A1: (9 |^ 2) + 1 = (a * b) * c ; :: according to NUMBER07:def 2 :: thesis: contradiction
9 |^ 2 = 9 * 9 by WSIERP_1:1;

per cases then ( ( a * b = 1 & c = 82 ) or ( a * b = 2 & c = 41 ) or ( a * b = 41 & c = 2 ) or ( a * b = 82 & c = 1 ) ) by A1, Th32;

suppose ( a * b = 1 & c = 82 ) ; :: thesis: contradiction

hence contradiction by XPRIMES0:82; :: thesis: verum

end;

suppose ( a * b = 2 & c = 41 ) ; :: thesis: contradiction

hence contradiction by XPRIMES1:2; :: thesis: verum

end;

suppose ( a * b = 41 & c = 2 ) ; :: thesis: contradiction

hence contradiction by XPRIMES1:41; :: thesis: verum

end;

suppose ( a * b = 82 & c = 1 ) ; :: thesis: contradiction

hence contradiction by XPRIMES0:1; :: thesis: verum

end;

end;