{{}} = dom op1 by FUNCT_2:def 1;
then {} in dom op1 by TARSKI:def 1;
then [{},(op1 . {})] in op1 by FUNCT_1:def 2;
then A1: {[{},(op1 . {})]} c= op1 by ZFMISC_1:31;
rng op1 = {(op1 . {})} by FUNCT_2:48;
then A2: op1 . {} = {} by ZFMISC_1:18;
op1 c= [:{{}},{{}}:] ;
then op1 c= {[{},{}]} by ZFMISC_1:29;
hence op1 = {[{},{}]} by A2, A1; :: thesis: verum