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;

theorem
  U1 in U2 or U1 = U2 or U2 in U1
proof
A1: On U1 in On U2 or On U1 = On U2 or On U2 in On U1 by ORDINAL1:14;
A2: U2 = Rank On U2 by Th50;
  U1 = Rank On U1 by Th50;
  hence thesis by A1,A2,CLASSES1:36;
end;
