reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;
reserve F,G for Cardinal-Function;
reserve A,B for set;

theorem
  for x1,x2,y1,y2 being set holds
  x1 in dom f & y1 in f.x1 & x2 in dom f & y2 in f.x2
  implies (x1,x2)-->(y1,y2) in sproduct f
proof
  let x1,x2,y1,y2 be set;
  assume that
A1: x1 in dom f and
A2: y1 in f.x1;
A3: x1 .--> y1 in sproduct f by A1,A2,Th60;
  assume that
A4: x2 in dom f and
A5: y2 in f.x2;
A6: x2 .--> y2 in sproduct f by A4,A5,Th60;
  (x1,x2)-->(y1,y2) = (x1 .--> y1) +* (x2 .--> y2) by FUNCT_4:def 4;
  hence thesis by A3,A6,Th70;
end;
