reserve X,Y,Z,X1,X2,Y1,Y2 for set, x,y,z,t,x1,x2 for object,
  f,g,h,f1,f2,g1,g2 for Function;

theorem
  rng f1 c= PFuncs(X,Y) & rng f2 c= PFuncs(X,Y) & not {} in rng f1 & not
  {} in rng f2 & uncurry f1 = uncurry f2 implies f1 = f2
proof
  assume that
A1: rng f1 c= PFuncs(X,Y) and
A2: rng f2 c= PFuncs(X,Y) and
A3: not {} in rng f1 and
A4: not {} in rng f2;
  curry uncurry f1 = f1 by A1,A3,Th44;
  hence thesis by A2,A4,Th44;
end;
