reserve A,B,C for Ordinal,
  X,X1,Y,Y1,Z for set,a,b,b1,b2,x,y,z for object,
  R for Relation,
  f,g,h for Function,
  k,m,n for Nat;
reserve M,N for Cardinal;

theorem Th17:
  A in nextcard A
proof
  assume not A in nextcard A;
  then
A1: card nextcard A c= card A by Th10,ORDINAL1:16;
A2: nextcard card A = nextcard A by Def2,Th16;
A3: card card A in nextcard card A by Def3;
  thus contradiction by A1,A2,A3,ORDINAL1:5;
end;
