Cooler Mash Tun tubing question...

So, I'm converting my cooler over and I went to Home Depot and picked up at 12" piece of braided stainless steel toilet supply line tube, a valve and 3' tubing.

After removing the braid I noticed that the tubing inside will fit perfectly (aka. very tightly) in the hole in the cooler. Thus saving me the money by allowing me to return the other 3' of tubing that I wouldn't need.

My question is: Is the tubing that is inside the SS toilet supply line going to work okay or will it cause problems? I've already filled the cooler half way with 168 degree water and ran it through. No leaks and it looks like it worked, but I'm going to defer to those with more experience than I.

You really want more than 12" of tubing on the outflow. A couple feet of drop will help to drain the MLT and siphon out the wort from the grain. I would think the inside of the supply line is food grade tubing??

That makes good sense. Thank you.