A1: omega c= Rank omega by CLASSES1:44;
then reconsider M = Rank omega as non empty set ;
0 in omega ;
then M is_Tarski-Class_of {} by A1, Th70, CLASSES1:def 3;
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 Th55, ORDINAL3:10;
A3: FinSETS = Rank (On FinSETS ) by Th54;
On FinSETS is limit_ordinal by Th55;
then omega c= On FinSETS by A2, ORDINAL1:def 12;
hence Rank omega c= FinSETS by A3, CLASSES1:43; :: thesis: verum