كتاب صلاة المسافرين وقصرها
6  
The Book of Prayer - Travellers
(17)
Chapter: Night prayers and the number of rak`ah offered by the Prophet (saws) at night, and that Witr is one rak`ah, and a one-rak`ah prayer is correct
(17)
باب صَلاَةِ اللَّيْلِ وَعَدَدِ رَكَعَاتِ النَّبِيِّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ فِي اللَّيْلِ وَأَنَّ الْوِتْرَ رَكْعَةٌ وَأَنَّ الرَّكْعَةَ صَلاَةٌ صَحِيحَةٌ
Sahih Muslim 739

'A'isha thus reported about the (night prayer) of the Messenger of Allah (ﷺ):

He used to sleep in the early part of the night, and woke up in the latter part. If he then wished intercourse with his wife, he satisfied his desire, and then went to sleep; and when the first call to prayer was made he jumped up (by Allah, she, i. e. 'A'isha, did not say" he stood up" ), and poured water over him (by Allah she, i. e. 'A'isha, did not say that he took a bath but I know what she meant) and if he did not have an intercourse, he performed ablution, just as a man performs ablution for prayer and then observed two rak'ahs.
وَحَدَّثَنَا أَحْمَدُ بْنُ يُونُسَ، حَدَّثَنَا زُهَيْرٌ، حَدَّثَنَا أَبُو إِسْحَاقَ، ح وَحَدَّثَنَا يَحْيَى بْنُ يَحْيَى، أَخْبَرَنَا أَبُو خَيْثَمَةَ، عَنْ أَبِي إِسْحَاقَ، قَالَ سَأَلْتُ الأَسْوَدَ بْنَ يَزِيدَ عَمَّا حَدَّثَتْهُ عَائِشَةُ، عَنْ صَلاَةِ، رَسُولِ اللَّهِ صلى الله عليه وسلم قَالَتْ كَانَ يَنَامُ أَوَّلَ اللَّيْلِ وَيُحْيِي آخِرَهُ ثُمَّ إِنْ كَانَتْ لَهُ حَاجَةٌ إِلَى أَهْلِهِ قَضَى حَاجَتَهُ ثُمَّ يَنَامُ فَإِذَا كَانَ عِنْدَ النِّدَاءِ الأَوَّلِ - قَالَتْ - وَثَبَ - وَلاَ وَاللَّهِ مَا قَالَتْ قَامَ - فَأَفَاضَ عَلَيْهِ الْمَاءَ - وَلاَ وَاللَّهِ مَا قَالَتِ اغْتَسَلَ ‏.‏ وَأَنَا أَعْلَمُ مَا تُرِيدُ - وَإِنْ لَمْ يَكُنْ جُنُبًا تَوَضَّأَ وُضُوءَ الرَّجُلِ لِلصَّلاَةِ ثُمَّ صَلَّى الرَّكْعَتَيْنِ ‏.‏
Reference : Sahih Muslim 739
In-book reference : Book 6, Hadith 157
USC-MSA web (English) reference : Book 4, Hadith 1612
  (deprecated numbering scheme)