I'm reading through Lurie's Higher Topos Theory and I'm not conviced by the proof of corollary 2.3.2.4. it asserts that it $i:A\rightarrow A'$ is inner anodyne and $j:B\rightarrow B'$ is a cofibration, then $$(A\times B')\coprod_{A\times B}(A'\times B)\rightarrow A'\times B'$$ is inner anodyne. How does the fact that the class of maps $A_3$ is stable under smash products with cofibrations can be extended to a statement about all inner anodyne maps?