Can I Tap Into Drain Pipe to Drain Condensate From High Efficiency Furnace

I just installed a high efficiency furnace in my unfinished basement. I want to use gravity instead of a pump to drain the condensate produced by the furnace. I have two drain pipes (a 2" and 1 1/2") that travel down the wall behind the furnace and into the concrete slab. I think one drains the washroom and the other a bathroom upstairs. Can I tap into one of these drain pipes with a y then run my condensate line into it? Would I need some kind of a p-trap, venting...The furnace uses 3/4" drain line.

It is no different than if you were installing a sink at that location. You will need a trap and it must be vented. Instead of a sink you would use a standpipe.

If the sewer ever backs up, it will come out the lowest point in the house, which might then be the standpipe.