let f1, f2 be Function of M,(M ./. R); :: thesis: ( ( for v being Element of M holds f1 . v = Class (R,v) ) & ( for v being Element of M holds f2 . v = Class (R,v) ) implies f1 = f2 )
assume that
A7: for v being Element of M holds f1 . v = Class (R,v) and
A8: for v being Element of M holds f2 . v = Class (R,v) ; :: thesis: f1 = f2

now :: thesis: for v being Element of M holds f1 . v = f2 . v

let v be Element of M; :: thesis: f1 . v = f2 . v
( f1 . v = Class (R,v) & f2 . v = Class (R,v) ) by A7, A8;
hence f1 . v = f2 . v ; :: thesis: verum

end;

hence f1 = f2 by FUNCT_2:63; :: thesis: verum