reserve k,n,m for Nat,
  A,B,C for Ordinal,
  X for set,
  x,y,z for object;
reserve f,g,h,fx for Function,
  K,M,N for Cardinal,
  phi,psi for
  Ordinal-Sequence;
reserve a,b for Aleph;

theorem Th23:
  omega c= cf a
proof
A1: a is_cofinal_with cf a by Def1;
  then cf a <> {} by ORDINAL2:50;
  then
A2: {} in cf a by ORDINAL3:8;
  cf a is limit_ordinal by A1,ORDINAL4:38;
  hence thesis by A2,ORDINAL1:def 11;
end;
