I have a question about the proof of Lemma 78.12.1 from Stacks Project. The aim of the last paragraph of the proof is to verify that the map of sheaves in the étale topology $F \to U/R$ is an isomorphism. By Lemma 7.11.2 our job is to show that it's surjective and injective. The proof that $F \to U/R$ is *injective* I not understand. The used argument is:

On the other hand, the map $F \to U/R$ is injective (as a map of presheaves) since $R=U \times_{U/R} U$ again by Spaces, Theorem 63.10.5.

Why $R=U \times_{U/R} U$ imply that the map is injective?