[KozmoNau7]

Dish soap is not dishwasher detergent.

Please don't put your pans in the dishwasher, not matter what they're made of.

[Xenograph]

I put my tri-ply stainless pans in the dishwasher all the time.

Why shouldn't I?

[balfirevic]

You should, it's 100% fine (and the main reason I prefer stainless to cast iron).

[tristor]

While stainless steel is “dishwasher safe”, dishwasher detergent is still overly harsh, can cause discoloration, and will prematurely wear the pan surface.