Mustadrak al-Hakim — Hadith 2980

It is narrated from Sayyiduna Abu Hurayrah and Sayyiduna Abu Sa'id al-Khudri (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) addressed us from the pulpit and said: "By the One in whose Hand is my soul." He (peace and blessings be upon him) said these words three times, then remained silent for a while. Every one of us began to weep in grief because of this (solemn) oath of the Messenger of Allah (peace and blessings be upon him). Then he (peace and blessings be upon him) said: "There is no servant who performs the five daily prayers regularly, fasts in Ramadan, and avoids the seven major sins, except that the gates of Paradise will be opened for him on the Day of Resurrection, until they (with joy and wideness) strike against one another." Then he (peace and blessings be upon him) recited this verse: "If you avoid the major sins which you are forbidden, We will remove from you your evil deeds" [Surah al-Nisa: 31].
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it.