set IntRel = {} ({{}},{{}});
for x being set st x in {{}} holds
not [x,x] in {} ({{}},{{}}) ;
then {} ({{}},{{}}) is_irreflexive_in {{}} by RELAT_2:def 2;
hence TrivAsymOrthoRelStr is irreflexive by Def12, CARD_1:49; :: thesis: verum