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 Th27:
  cf a in a implies a is limit_cardinal
proof
  assume
A1: cf a in a;
  given M such that
A2: a = nextcard M;
  cf a c= M by A1,A2,CARD_3:91;
  then reconsider M as Aleph;
  nextcard M in nextcard M by A1,A2,Th22;
  hence contradiction;
end;
