The Gibbard–Satterthwaite Theorem

Sketch (reduction to Arrow's theorem). First, a monotonicity lemma: if alternative $a$ wins at some profile, and the profile changes only by some voters moving $a$ higher in their own ranking (without otherwise reordering the other alternatives), $a$ must still win. Otherwise a voter whose sincere ranking is the "before" profile could misreport as the "after" profile to push $a$ from losing to winning, or vice versa — either way, contradicting strategy-proofness for someone.

Next, use the choice function to build a derived social ranking for each profile: declare $a$ above $b$ in the derived ranking exactly when $a$ would still win after every alternative other than $a$ and $b$ is deleted from every voter's ballot, leaving a straight two-way race. Ontoness and strategy-proofness of the original choice function, together with the monotonicity lemma, can be used to check that this derived ranking satisfies Unrestricted Domain, Weak Pareto, and Independence of Irrelevant Alternatives as a social welfare function.

By Arrow's Impossibility Theorem, since there are at least $3$ alternatives, this derived social ranking must be dictatorial: some voter $i$'s ranking always equals the derived social ranking.

Finally, check that this same voter $i$'s top choice is always the winner of the original social choice function: since the derived ranking puts $i$'s favorite alternative above every other alternative, and the derived ranking tracks who wins pairwise comparisons, $i$'s favorite must be the overall winner at every profile. So the original strategy-proof, onto social choice function is dictated by voter $i$.