In the textbook, `Electronic Devices and Circuit Theory, 11th Edition by Boylestead and Nashelsky`, on page 566, the lower cutoff frequency is derived for a voltage divider BJT circuit. The circuit used is shown below.

[![Voltage Divider BJT Circuit](https://i.stack.imgur.com/O3GGy.png)](https://i.stack.imgur.com/O3GGy.png)

The lower cutoff frequency of \$C\_E\$ is to be found. For this, they first find the equivalent AC circuit as seen from \$C\_E\$. 

[![AC Equivalent Circuit](https://i.stack.imgur.com/Ax3uV.png)](https://i.stack.imgur.com/Ax3uV.png)

My question is, how did the obtain this expression?: $$\dfrac{R\_1||R\_2}{\beta}+r\_e$$

I understand that they applied Thevenin's thorem, but I'm stil not sure how this expression comes out. Also, doesn't \$R\_C\$ play a role here?