I have a set of sets S that is closed under the set-theoretic operations of union, intersection, and complement, so it basically forms a Boolean algebra with the join operator being union, the meet operator being intersection, and the complement operator being set complement.
Then, I have three subsets A, B, and C of set S.
I know that if A $\subseteq$ B and A $\subseteq$ C then A $\subseteq$ B $\cap$ C.
I do not want to prove that property/law, I just want to use it in my manuscript, but does it have a name?
I found in wikipedia that it is called "existence of meets" (wiki), so is it correct if I say that "As A $\subseteq$ B and A $\subseteq$ C, it holds that A $\subseteq$ B $\cap$ C by existence of meets." or is there a better suggestion?