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Tarski's caracterisation of inaccessible cardinals

Alfred Tarski, in his paper "Ueber unerreichbare Kardinalzahlen" Fund. Math. vol 30 (1938) pp 68-89 proves the followig theorem of ZFC "If the cardinal of the set Y is equal to the cardinal of the set of the subsets of Y that are not equipotent with Y, then the cardinal of Y is (strongly) inaccessible". The proof of the paper is rather long and involved. Question: Is there another known simpler proof of this theorem ? Gérard Lang