reserve n for Element of NAT,
  p,q,r,s for Element of HP-WFF;

theorem Th10:
  for a,b,x,y,X,Y being set st a<>b & x in X & y in Y holds
  (a,b) --> (x,y) in product((a,b) --> (X,Y))
proof
  let a,b,x,y,X,Y be set such that
A1: a<>b and
A2: x in X & y in Y;
  {x} c= X & {y} c= Y by A2,ZFMISC_1:31;
  then product((a,b) --> ({x},{y})) c= product((a,b) --> (X,Y)) by TOPREAL6:21;
  then {(a,b) -->(x,y)} c= product((a,b) --> (X,Y)) by A1,CARD_3:47;
  hence thesis by ZFMISC_1:31;
end;
