reserve A,B for Ordinal,
  K,M,N for Cardinal,
  x,x1,x2,y,y1,y2,z,u for object,X,Y,Z,X1,X2, Y1,Y2 for set,
  f,g for Function;
reserve m,n for Nat;

theorem Th41:
  for X being set holds card X = 1 iff ex x being object st X = {x}
proof
  let X be set;
  card {0} = 1 by CARD_1:30;
  hence card X = 1 implies ex x being object st X = {x} by CARD_1:29;
  given x being object such that
A1: X = {x};
  thus thesis by A1,CARD_1:30;
end;
