Caution: Translations of Quran and Ḥadīth may lead to possible misapplications and misinterpretations. This site is intended for students of sacred knowledge that are proficient in comprehending classical Arabic and have a strong foundation in Islamic sciences. Also note that religious injunctions rely on several aspects beyond what one may glean through reading individual aḥādīth.
suyuti:7748a
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السيوطي:٧٧٤٨a

"إِنَّمَا جُعِلَ الأَذانُ الأوَّلُ لِتَيَسُّرِ أَهْل الصَّلاة لصلاتهم، فإِذا سمعتم الأَذانَ فأسْبِغُوا الوضوءَ وإِذا سَمِعْتَم الإِقامَةَ فبادِروا التَّكبيرةَ الأُولَى، فإِنَّها فَرْعُ الصَّلاةِ وتمامُهَا، ولا تبادروا القارئَ الرُّكُوعَ والسُّجودَ".  

[طب] الطبرانى في الكبير عن ابن عباس

See similar narrations below:

Collected by Ṭabarānī
tabarani:12383Muḥammad b. ʿAbdullāh al-Ḥaḍramī

[Machine] The Messenger of Allah ﷺ said, "The first Adhan was made only to make it easier for the people of prayer to prepare for their prayer. So when you hear the Adhan, perfect your ablution, and when you hear the Iqamah, hurry to make the first Takbir, as it is the branch of the prayer and its completion. Do not precede the reciter in bowing and prostrating."  

الطبراني:١٢٣٨٣حَدَّثَنَا مُحَمَّدُ بْنُ عَبْدِ اللهِ الْحَضْرَمِيُّ ثنا إِسْمَاعِيلُ بْنُ أَبِي الْحَكَمِ الثَّقَفِيُّ ثنا عَاصِمُ بْنُ مُضَرِّسٍ النَّصْرِيُّ عَنْ جَبَلَةَ بْنِ سُلَيْمَانَ عَنْ سَعِيدِ بْنِ جُبَيْرٍ عَنِ ابْنِ عَبَّاسٍ قَالَ

قَالَ رَسُولُ اللهِ ﷺ «إِنَّمَا جُعِلَ الْأَذَانُ الْأَوَّلُ لِيَتَيَسَّرَ أَهْلُ الصَّلَاةِ لِصَلَاتِهِمْ فَإِذَا سَمِعْتُمُ الْأَذَانَ فَأَسْبِغُوا الْوُضُوءَ وَإِذَا سَمِعْتُمُ الْإِقَامَةَ فَبَادِرُوا التَّكْبِيرَةَ الْأُولَى فَإِنَّهَا فَرْعُ الصَّلَاةِ وَتَمَامُهَا وَلَا تُبَادِرُوا الْقَارِئَ الرُّكُوعَ وَالسُّجُودَ»