Water is due to water

It is narrated from Sayyiduna Ali (may Allah be pleased with him) that a man asked him: What is the ruling if a man has intercourse with his wife and does not ejaculate (emit semen)? He (may Allah be pleased with him) said: "Even if he moves her so much that the hair of her head (or both sides of her head) shakes from the intensity of the motion, ghusl is not obligatory upon him."

It is narrated from Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) that he said: "If I reached that (point of intercourse) with my wife, I would certainly take a bath."
Musaddad transmitted this hadith through Yahya, Shu'bah, Mansur and Hilal bin Yasaf from Kharashah bin Habib, who narrated it from Ali (may Allah be pleased with him); and Sufyan narrated it through Sulayman and Mansur from Ibrahim, he from Alqamah, and he from Abdullah bin Mas'ud (may Allah be pleased with him); while in another route Abdullah bin Dawud narrated it from al-A'mash, and he from Ibrahim, but here Imam al-A'mash was in doubt about the link through Alqamah.

It is narrated from Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) that he said: "The obligation of ghusl (that is, the use of water) arises only from the emission of semen (that is, the coming out of water), and there is no harm in (impurity on the garment or body) amounting to one or two dirhams."
This narration is sahih (authentic) and reliable in its chain. The first rule mentioned in it, "al-ma' min al-ma'" (water is from water), was among the rulings of the early period of Islam, which was later abrogated in the case of intercourse by mere penetration (even without ejaculation); while the matter of pardoning a small amount of impurity (the size of a dirham) holds importance among the jurists in the chapter on purification.

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that he said: "Water (the obligation of ghusl) is only because of water (the emission of semen)."
This narration is sahih (authentic) and mawquf (a Companion's statement).

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) sent a message summoning a man from the Ansar, and he was somewhat late in coming. (When he arrived) he (peace and blessings be upon him) asked him: "What held you back?" He said: O Messenger of Allah! When your messenger came to me, I was engaged in intimacy with my wife; then I got up and took a bath (which is why I was late). He (peace and blessings be upon him) said: "If you did not ejaculate, it was not obligatory upon you to take a bath." Sayyiduna Ibn Abbas (may Allah be pleased with them both) says: Then for a period the Ansar acted upon this.
Abu Sa'd means Sa'id bin al-Marzuban al-Baqqal, and he is a weak narrator.

Abu Salamah bin Abd al-Rahman (may Allah have mercy on him) narrates from his father (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) went looking for a man from the Ansar and called him. The Ansari Companion came out with drops of the bath water dripping from his head. The Messenger of Allah (peace and blessings be upon him) asked him: "What troubled you?" (that is, what was the reason for such haste?) He said: (O Messenger of Allah!) You called me when I was with my wife, and I feared that I might be late in presenting myself to you, so I hurried, got up, poured water over myself and came out at once. He (peace and blessings be upon him) asked: "Did you ejaculate?" He replied: No. At this he (peace and blessings be upon him) said: "When you do that (that is, there is no ejaculation during intercourse), do not take a bath; rather wash the part (of your body) that touched (the body of) the woman, and then perform ablution as for prayer, for water (that is, ghusl) is required only because of water (that is, the emission of semen)."
The ruling mentioned in this hadith, "water is from water" (that is, ghusl becomes obligatory only by the emission of semen), belongs to the early period of Islam; it was later "abrogated or clarified by the saying of the Prophet (peace and blessings be upon him) that when the two private parts meet (that is, penetration occurs), ghusl becomes obligatory whether there is ejaculation or not". The takhrij of this hadith is in Sahih Muslim (343) and Sunan Abi Dawud (215).