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 Th40:
  for X being finite set st not x in X holds card (X \/ {x}) = card X + 1
proof
  let X be finite set;
A1: card {x} = 1 by CARD_1:30;
  assume not x in X;
  hence thesis by A1,Th39,ZFMISC_1:50;
end;
