Vent distance to bathroom sink
We have an unfinished room in the basement that is plumbed for a 1-sink bathroom. I don't like the current position of the sink drain and would like to move it. The trouble is (I think), that its new proposed position would make the sink trap too far (more than 3' 6") from the current vent position. The drain pipe diameter is 1-1/2 inches. (Please correct me if I've misunderstood the required trap-to-vent distance).
My question: Am I allowed to move the vent such that its connection to the drain is within the required 3' 6" of the new sink trap. Please look at the "Current" and "Proposed" diagrams below for clarification. Thanks very much for any help.