Remark 6.2.2.5. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing a commutative diagram
\[ \xymatrix@C =50pt@R=50pt{ & Y \ar [dr]^{v} & \\ X \ar [ur]^{u} \ar [rr]^{w} & & Z } \]
and let $\operatorname{\mathcal{C}}' \subseteq \operatorname{\mathcal{C}}$ be a full subcategory. If any two of the morphisms $u$, $v$, and $w$ are $\operatorname{\mathcal{C}}'$-local equivalences, then so is the third.