reserve A,B,C for Ordinal;
reserve a,b,c,d for natural Ordinal;
reserve l,m,n for natural Ordinal;
reserve i,j,k for Element of omega;
reserve x,y,z for Element of RAT+;

theorem Th32:
  not ex i,j being object st [i,j] in omega
proof
  given i,j being object such that
A1: [i,j] in omega;
  reconsider a = [i,j] as Element of omega by A1;
  {} in a by ORDINAL3:8;
  hence thesis by TARSKI:def 2;
end;
