reserve A,B for limit_ordinal infinite Ordinal;
reserve B1,B2,B3,B5,B6,D, C for Ordinal;
reserve X for set;
reserve X for Subset of A;
reserve M for non countable Aleph;
reserve X for Subset of M;
reserve N,N1 for cardinal infinite Element of M;
reserve A for Ordinal;
reserve x,y,X,Y for set;

theorem Th37:
  for A being non empty Ordinal holds Rank A is non empty
proof
  let A be non empty Ordinal;
  {} c= A;
  then {} c< A by XBOOLE_0:def 8;
  then {} in A by ORDINAL1:11;
  hence thesis by CLASSES1:36;
end;
