let f1, f2 be Function of L,L; :: thesis: ( ( for y being Element of L holds f1 . y = x * (power (y,n)) ) & ( for y being Element of L holds f2 . y = x * (power (y,n)) ) implies f1 = f2 )
assume that
A2: for y being Element of L holds f1 . y = x * (power (y,n)) and
A3: for y being Element of L holds f2 . y = x * (power (y,n)) ; :: thesis: f1 = f2

now :: thesis: for y being Element of L holds f1 . y = f2 . y

let y be Element of L; :: thesis: f1 . y = f2 . y
thus f1 . y = x * (power (y,n)) by A2
.= f2 . y by A3 ; :: thesis: verum

end;

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