Two-voter dictatorship from binary choice

For two voters and at least three alternatives, pairwise unanimity, pairwise independence and transitivity force the binary social ordering from strategyproof choice to follow one fixed voter. If voter one wins a conflict $a$ against $b$, use profiles $(a>b>c,b>c>a)$ and $(c>a>b,b>c>a)$ to show it also wins $a$ against $c$ and $c$ against $b$. Repeating this implication yields both directions of every pair. If the initial conflict instead follows voter two, exchange the roles. The social choice, being the top of that ordering, is a dictatorship in social choice. This proves the two-voter case of the Gibbard-Satterthwaite theorem.