“If one of you wakes up from sleep and finds moisture but does not recall having had a wet dream, let him perform ghusl; and if he recalls having had a wet dream but finds no moisture, then no ghusl is required.”

Narrated by Aḥmad (no. 26195), al-Tirmidhī (no. 113), and Ibn Mājah (no. 612) — the wording is his — from the narration of ʿĀʾishah –may Allah be pleased with her–.
Authenticated in Ṣaḥīḥ al-Jāmiʿ (no. 330) and Ṣaḥīḥ Ibn Mājah (no. 502).

Brief Explanation of the Hadith

A Muslim should understand the matters upon which the validity of his worship depends. Among these is knowing the causes that necessitate the ritual bath (ghusl) from major impurity, and when it becomes obligatory.
In this ḥadīth, the Prophet –may Allah’s peace and blessings be upon him– informs that whoever wakes up from his sleep and finds traces of semen on his body or clothes must perform ghusl. Whether he remembers having had a wet dream or not, this is by consensus of the scholars, because the presence of the wetness is sufficient evidence of the emission of semen. However, if he saw in his dream that he had a wet dream but found no wetness, then there is no ghusl upon him by consensus of the scholars, because ghusl is only obligatory when semen has actually been emitted.
This ḥadīth therefore indicates that ghusl is connected to the actual presence of semen, whether or not one remembers having had a wet dream, and that merely seeing a wet dream does not necessitate ghusl unless accompanied by ejaculation.
It also shows that Islamic rulings are based on certainty, not on doubt or conjecture, so ghusl is not required merely due to suspicion or assumption. The ḥadīth further indicates that clarifying what people need to know regarding the rulings of purification and worship carries no blame; rather, it is part of conveying knowledge and teaching the religion.