I remember encountering a (probably Latin) word/phrase which is used when you prove something stronger than what was desired, and therefore our desired claim follows. I like to collect mots justes, and so I would appreciate anyone helping me remember this one.
As an example: suppose for two finite sets $A$ and $B$, you want to show that $|A| \le |B|$. One way to do that would be to show $A \subseteq B$, from which $|A| \le |B|$ follows. Now we have proved something stronger in order to show our inequality, and in order to finish our proof we ended with a remark saying "from which $|A| \le |B|$ follows" and I want to say instead "[unknown word here] $|A| \le |B|$".