Apple Hardware Test for mid 2010 MacBook Pro

If your machine has received the proper updates, you might be able to run AHT through Internet Recovery by holding down option-D at power on. The following says the machine should have shipped with Lion for this to be enabled, although I'm not sure if perhaps the Internet Recovery capability would also allow for option-D to work.

How to use Apple Hardware Test on your Mac - Apple Support

Other than that, perhaps read this topic for how to create a bootable AHT flash drive. I followed the instructions and have AHT located on a small (100 MB) USB flash drive partition. It requires copying over a directory and them making the USB flash drive bootable. It would need to be connected at power up with option held down. Then it would selected from a list of bootable partitions.

Did I remove Apple Hardware Test with SSD upgrade?

This site:

https://github.com/upekkha/AppleHardwareTest

The easiest way to proceed is to place it on a USB stick and "bless" the usb stick so you can boot from it. There are also directions for blessing it once you place it back in the "factory" position:

/System/Library/CoreServices/.diagnostics ...

... but manipulating invisible directories protected by System Integrity Protection can be very difficult.

If you are running Sierra as your specs say, then try booting into Apple Hardware Test from your hard drive holding the "d" key at startup :

How to use Apple Hardware Test on your Mac - Apple Support