All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
What is meant from this expression is that Al-Haakim classified a particular Hadeeth as Saheeh in his “Al-Mustadrak” and Ath-Thahabi agreed with him in classifying this Hadeeth as Saheeh.
As for Ath-Thahabi, he is Imaam Al-Haafith Shams Ad-Deen Muhammad ibn Ahmad ibn ‘Uthmaan Ath-Thahabi and he was originally from Turkmenistan. He was born in the town of Meiafarakin, a district of Diyarbakr, a province of Turkey, in Rabee’ Al-Aakhir 673 A.H. Among his books are: “Siyar A’laam An-Nubalaa’”, “Taareekh Al-Islaam”, and both are history books, and “Tathkiratul Huffaath” and “Mizaan Al-I’tidaal” which are biography books.
As regards his relation with “Al-Mustadrak” of Al-Haakim, then he checked its Ahaadeeth and clarified the things on which Al-Haakim was right and the things in which Al-Haakim was wrong. That is because Al-Haakim Thahabi ruled all the Ahaadeeth of “Al-Mustadrak” to be authentic according the conditions of Al-Bukhari and Muslim and he actually mentioned many Saheeh and Hasan Ahaadeeth, but he was wrong when he mentioned many Dha’eef Ahadeeth and even some Munkar [denounced] or fabricated Ahaadeeth, and Ath-Thahabi complied a book about this which he entitled “At-Talkhees”.
Allaah Knows best.