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The article provides two short and direct proofs of J. S. Pym's result in his 1969 paper "The linking of sets in graphs," regarding the Cantor-Bernstein theorem for paths in graphs. Both proofs are elementary, and they can be examined independently. The first proof employs transfinite induction. This proof starts from the first set of paths which is then transformed step by step into the wanted bijective set by integrating path segments from the second set. The choices made during this inductive process have been made arbitrary. For the second proof, these choices are made explicitly.