Muslim relates this report in full under the heading “The Sin of the One Who Withholds the Zakah” 1, and it proves that such a person is not deemed a disbeliever; for had he been a disbeliever, no route to Paradise would remain open to him. Accordingly, the explicit wording of this ḥadith takes precedence over the inferred meaning of the verse in Sūrat al-Tawbah, because in legal theory an explicit text outweighs an implicit indication.
Second: Proofs from the Sunnah
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The Prophet ﷺ said, “Between a man and polytheism and disbelief lies the abandonment of the prayer.” Reported by Muslim in the Book of Faith, on the authority of Jābir ibn ʿAbd Allāh 2.
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Buraidah ibn al-Ḥusayb (may Allah be pleased with him) narrated: “I heard the Messenger of Allah ﷺ say, ‘The covenant that distinguishes us from them is the prayer; whoever abandons it has disbelieved.’” Reported by Aḥmad, Abū Dāwūd, al-Tirmidhī, al-Nasāʾī, and Ibn Mājah 3.