given a, b, c being Prime such that a,b,c are_mutually_distinct and
A1: (1 |^ 2) + 1 = (a * b) * c ; :: according to NUMBER07:def 2 :: thesis: contradiction
( ( a * b = 1 & c = 2 ) or ( a * b = 2 & c = 1 ) ) by A1, Th26, XPRIMES1:2;
hence contradiction by XPRIMES1:2, NAT_1:15; :: thesis: verum