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;
reserve S for Sequence;

theorem Th34:
  succ X, succ Y are_equipotent implies X, Y are_equipotent
proof
A1: X in succ X & Y in succ Y by ORDINAL1:6;
  X = succ X \ {X} & Y = succ Y \ {Y} by ORDINAL1:37;
  hence thesis by A1,Th33;
end;
