وَتِلْكَ عَادٌ جَحَدُواْ بِأيَاتِ رَبِّهِمْ وَعَصَوْاْ رُسُلَهُ
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Such were `Ad (people). They rejected the Ayat of their Lord, and disobeyed His Messengers,
This means they disbelieved in the proofs and revelations (of Allah) and they disobeyed the Messengers of Allah.
This is due to the fact that whoever disbelieves in a Prophet, then verily, he has disbelieved in all of the Prophets, peace be upon them. There is no difference between any one of them, in the sense that it is necessary to believe in all of them. Therefore, `Ad disbelieved in Hud and their disbelief was considered disbelief in all of the Messengers.
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وَاتَّبَعُواْ أَمْرَ كُلِّ جَبَّارٍ عَنِيدٍ
and followed the command of every proud, obstinate.
This means that they abandoned following their rightly guided Messenger and they followed the command of every proud, obstinate person. Thus, they were followed in this life by a curse from Allah and His believing servants whenever they are mentioned. On the Day of Resurrection a call will be made against them in front of witnesses.