Cantor-Bernstein Implies Excluded Middle

We prove in constructive logic that the statement of the Cantor-Bernstein theorem implies excluded middle. This establishes that the Cantor-Bernstein theorem can only be proven assuming the full power of classical logic. The key ingredient is a theorem of Martín Escardó stating that quantification over a particular subset of the Cantor space 2^ℕ, the so-called one-point compactification of ℕ, preserves decidable predicates.