Holding penalty versus personal foul

The offence runs the ball for a first down on a 3rd and 10 play and the officials call holding on the offence, and there is also a personal foul called against to offence that was said to be a dead ball foul. So question was do they assess both fouls or one of the two. The explanation was that the defence could either take the 10 yard holding call or decline it and than take the dead ball personal foul for 15 yards. The defence chose to take the 15 yard dead ball foul.

My question is in that case wouldn't the 10 yard first down run than count as that penalty was declined making it 1st and 15 rather than 3rd and 25. In any other case if a penalty is declined the yardage occurred in that play stands.