MOS current mirror with Early Effect formula derivation

[Starhowl]

The current mirror ratio

I_o/I_REF = ((W/L)_1 / (W/L)_2) * (1 + lambda*V_DS1)*(1 + lambda * V_DS2)

can also be expressed as

I_o/I_REF = ((W/L)_1 / (W/L)_2) * (1 + (V_o - V_GS)/V_A),

which implies that

(1 + lambda*V_DS1)*(1 + lambda * V_DS2) = (1 + (V_o - V_GS)/V_A).

Can someone explain to me why?

(You can see the identity on page 5 of the attached PDF or on p. 529 of Microelectronic Circuits)