This paper considers social choice correspondences assigning a choice set to each non-empty subset of social alternatives. We impose three requirements on these correspondences: unanimity, independence of preferences over infeasible alternatives and choice consistency with respect to choices out of all possible alternatives. With more than three social alternatives and the universal preference domain, any social choice correspondence that satisfies our requirements is serially dictatorial. A number of known impossibility theorems — including Arrow’s Impossibility Theorem, the Muller-Satterthwaite Theorem and the impossibility theorem under strategic candidacy — follow as corollaries. Our new proof highlights the common logical underpinnings behind these theorems.