Could you explain a bit why slew rate is calculated by that formula along with that assumption?

I know that slew rate is defined as the maximum rate of change of output voltage per unit of time and is expressed as volt per second.
However, the lecture below give that formula without any explanation is a bit confusing.

The output of the first stage is very small compared to that of the second stage. So, voltage across C_c is approximately output voltage. When I5 flows through this capacitor, output voltage ramps up/down with slope I5/C_c. I5 is the maximum source/sink current from the first stage which flows through C_c. The assumption that I7>>I5 is there because the slew rate is not limited by the second stage current.