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
  X c= Y & Y c= Z & X,Z are_equipotent implies X,Y are_equipotent & Y,Z
  are_equipotent
proof
  assume that
A1: X c= Y & Y c= Z and
A2: X,Z are_equipotent;
A3: card X = card Z by A2,Th4;
  card X c= card Y & card Y c= card Z by A1,Th10;
  hence thesis by A3,Th4,XBOOLE_0:def 10;
end;
