[{},{}] in [:{{}},{{}}:] by ZFMISC_1:34;
hence op2 . ({},{}) = {} by CARD_1:87, FUNCT_2:65; :: thesis: ( op1 . {} = {} & op0 = {} )
{} in {{}} by TARSKI:def 1;
hence op1 . {} = {} by CARD_1:87, FUNCT_2:65; :: thesis: op0 = {}
thus op0 = {} ; :: thesis: verum