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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
We can reconcile between the two matters by saying that the definition of Shaykh Muhammad ibn ‘Abdul Wahhaab in his book Al-Usool Ath-Thalaathah (Three Fundamental Principles) is about Islam in general which is the comprehensive religion of Islam, Eemaan (faith), and Ihsaan (perfection and excellence of worship) while the Hadeeth is about Islam in its particular meaning. Therefore, he said after the stated definition: “There are three degrees of Islam, which are: Islam, Eemaan and Ihsaan. Each of them has its certain pillars.”
Nevertheless, the definition of Shaykh Muhammad ibn ‘Abdul Wahhaab is derived from what was mentioned in the stated Hadeeth and that of Jibreel (Gabriel) . That is because whoever bears witness that there is none worthy of worship besides Allaah has disassociated himself from Shirk (polytheism), submitted himself to Tawheed (monotheism), and whoever fulfills the remaining pillars such as prayer and the like has submitted himself to obedience.
It was stated in Sharh At-Tahaawiyyah by Ibn Jibreen: “The meaning of Islam according to Sharee‘ah terminology is very close to its linguistic meaning. Shaykh Muhammad ibn ‘Abdul Wahhaab, defined it at the beginning of Al-Usool saying: “Islam is to submit to Allaah by affirming that He is One, and to surrender to Him by obeying Him and disavowing Shirk and its people. That is the meaning of Islam which is very close to its linguistic meaning which is submission and surrender. As for its meaning according to Sharee‘ah terminology, nothing is clearer than the definition which the Prophet, sallallaahu ‘alayhi wa sallam, gave by naming these five pillars because they are the best proof for one’s submission, surrender and commitment, for whoever adheres firmly to those pillars, he will surrender to his Lord and will not disobey Him and he will do them with clear submissiveness as if he is led by reins.”
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Allaah Knows best.