reserve m for Cardinal,
  A,B,C for Ordinal,
  x,y,z,X,Y,Z,W for set,
  f for Function;
reserve f,g for Function,
  L for Sequence,
  F for Cardinal-Function;
reserve U1,U2,U for Universe;
reserve u,v for Element of U;

theorem
  FinSETS c= U & Tarski-Class {} c= U & UNIVERSE {} c= U
proof
A1: On U c= Rank On U by CLASSES1:38;
A2: Rank On U = U by Th50;
  {} in On U by Th51,ORDINAL3:8;
  hence thesis by A2,A1,Lm6,Th4;
end;
