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;

theorem Th7:
  X1,Y1 are_equipotent & X2,Y2 are_equipotent implies [:X1,X2:],[:
  Y1,Y2:] are_equipotent & card [:X1,X2:] = card [:Y1,Y2:]
proof
  assume X1,Y1 are_equipotent & X2,Y2 are_equipotent;
  then
A1: card X1 = card Y1 & card X2 = card Y2 by CARD_1:5;
  [:X1,X2:],[:card X1,card X2:] are_equipotent & [:Y1,Y2:],[:card Y1,card
  Y2:] are_equipotent by Th6;
  hence [:X1,X2:],[:Y1,Y2:] are_equipotent by A1,WELLORD2:15;
  hence thesis by CARD_1:5;
end;
