Imagine a Vertical 4" pipe coming up the basement wall and making a Wye about 1 ft from the ceiling..
Left to the 2nd floor toilet and sink.
Right is going to the 1st floor toilet, about 2 ft away. (and 1st floor sink and bathtub)
Up against the ceiling is a 2" vent pipe coming from the basement plumbing and heading to the roof. (turning into a 4")
So, if I connect the waste pipe up to the 2" vent pipe, would that satify the venting for the 1st floor toilet?
This will be a 2" from the 4" waste, to the 2" vent. But it will be about 1ft long.
Is this a satisfactory vent?
It sounds logical, but I've never seen is done like that.
The 2" vent from the basement washroom can be used for the 1st floor vent if you join the 2" vent to the 1st floor vents at least 6" above the fixture flood rims...
This means that you cannot join the vents together until about 42" above the 1st floor bathroom floor...
If it is just the toilet you need to vent on this 2" pipe, measure from the floor to the rim of the WC and add 6"... That is the lowest you can join into the existing 2" vent.
What you descsribe, and it is not as clear as you intended it to be, can work. The key word being "can" because whether it would be correct or not depends entirely on how you actually install the piping. Is this a new first floor bathroom, in which case you may be describing an improper drain connection, or for a new basement bath. You do not tell what you need this vent connection for, or why.