A1: {} is Subset of X by XBOOLE_1:2;
A2: {{} ,{} } = {{} } by ENUMSET1:69;
A3: {} in S by PROB_1:10;
reconsider C = {{} } as N_Sub_set_fam of X by A1, A2, MEASURE1:41;
take C ; :: thesis: C c= S
thus C c= S by A3, ZFMISC_1:37; :: thesis: verum