[(In 1,2),(In 1,2)] in dom (1,1 .--> 1) by Lm2, Lm10, TARSKI:def 1;
hence mult_2 . (In 1,2),(In 1,2) = (1,1 .--> 1) . (In 1,2),(In 1,2) by FUNCT_4:14
.= In 1,2 by Lm2, FUNCOP_1:86 ;
:: thesis: verum