Washing away what comes out from the private parts of a woman (woman‘s discharge) if one gets soiled with that

Narrated Zaid bin Khalid AjJuhani:

I asked 'Uthman bin 'Affan about a man who engaged in the sexual intercourse with his wife but did not discharge. 'Uthman replied, "He should perform ablution like that for the prayer after washing his private parts." 'Uthman added, "I heard that from Allah's Apostle." I asked 'Ali bin Abi Talib, Az-Zubair bin Al-'Awwam, Talha bin 'Ubaidullah and Ubai bin Ka'b and a gave the same reply. (Abu Aiylub said that he had heard that from Allah's Apostle ) (This order was cancelled later on so one has to take a bath. See, Hadith No. 180).

حَدَّثَنَا أَبُو مَعْمَرٍ، حَدَّثَنَا عَبْدُ الْوَارِثِ، عَنِ الْحُسَيْنِ، قَالَ يَحْيَى وَأَخْبَرَنِي أَبُو سَلَمَةَ، أَنَّ عَطَاءَ بْنَ يَسَارٍ، أَخْبَرَهُ أَنَّ زَيْدَ بْنَ خَالِدٍ الْجُهَنِيَّ أَخْبَرَهُ أَنَّهُ، سَأَلَ عُثْمَانَ بْنَ عَفَّانَ فَقَالَ أَرَأَيْتَ إِذَا جَامَعَ الرَّجُلُ امْرَأَتَهُ فَلَمْ يُمْنِ. قَالَ عُثْمَانُ يَتَوَضَّأُ كَمَا يَتَوَضَّأُ لِلصَّلاَةِ، وَيَغْسِلُ ذَكَرَهُ. قَالَ عُثْمَانُ سَمِعْتُهُ مِنْ رَسُولِ اللَّهِ ﷺ. فَسَأَلْتُ عَنْ ذَلِكَ عَلِيَّ بْنَ أَبِي طَالِبٍ وَالزُّبَيْرَ بْنَ الْعَوَّامِ وَطَلْحَةَ بْنَ عُبَيْدِ اللَّهِ وَأُبَىَّ بْنَ كَعْبٍ ـ رضى الله عنهم ـ فَأَمَرُوهُ بِذَلِكَ. قَالَ يَحْيَى وَأَخْبَرَنِي أَبُو سَلَمَةَ أَنَّ عُرْوَةَ بْنَ الزُّبَيْرِ أَخْبَرَهُ أَنَّ أَبَا أَيُّوبَ أَخْبَرَهُ أَنَّهُ سَمِعَ ذَلِكَ مِنْ رَسُولِ اللَّهِ ﷺ.