A1: omega c= Rank omega by CLASSES1:38;
then reconsider M = Rank omega as non empty set ;
0 in omega ;
then M is_Tarski-Class_of {} by A1, Th63;
hence FinSETS c= Rank omega by CLASSES1:def 4; :: according to XBOOLE_0:def 10 :: thesis: Rank omega c= FinSETS
A2: {} in On FinSETS by Th51, ORDINAL3:8;
A3: FinSETS = Rank (On FinSETS) by Th50;
On FinSETS is limit_ordinal by Th51;
then omega c= On FinSETS by A2, ORDINAL1:def 11;
hence Rank omega c= FinSETS by A3, CLASSES1:37; :: thesis: verum