reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem
  X1 c= X2 & Y1 c= Y2 implies PFuncs(X1,Y1) c= PFuncs(X2,Y2)
proof
  assume
A1: X1 c= X2 & Y1 c= Y2;
  let f be object;
  assume f in PFuncs(X1,Y1);
  then f is PartFunc of X1,Y1 by Th46;
  then f is PartFunc of X2,Y2 by A1,RELSET_1:7;
  hence thesis by Th45;
end;
