Let f(R,S) be the image of a pair of fuzzy subsets constructed by applying Zadeh's (1975) extension principle to a function of two variables. Nguyen (1978) gave a necessary and sufficient condition for the α-cuts of f(R,S) to be equal to the crisp images of the α-cuts of R,S. Here we give a simplified proof of this theorem which also holds in a more general context: particularly for second-order fuzzy subsets.