Is it normal to not feel so bad about putting my dog down?

I adopted a 6 year old dog, who had been abused pretty badly. He was afraid of everyone he didn't know, and anything that moved fast or made noise. I had him for 9 years. He was 15 years old when I put him down yesterday. I felt it was best because between finding out that he had both cancer and congestive heart failure, and being so old anyway, there was no way I could keep him from dying. I honestly didn't expect him to live past 12, since he's fairly big and my other dogs only lived to be 8 and 11. He was mostly deaf, and for the past few years, there were days I would come home and he wouldn't come to the door because he was sleeping somewhere, and each time I immediately panicked, worrying something had happened. He's always been afraid to be alone, so I never wanted him to die alone. But I wasn't going to put him down for no reason. So once we figured out he was really sick, and he stopped eating, I figured it was time. I made the appointment for early evening, the vet was nice enough to schedule it for the time when the clinic usually closes, so that way there was no one else there. I spent the whole day with him (which was a bit depressing knowing what was coming, but I did it for his sake) and let him eat anything he wanted. I took some pictures of me and him together, and then when I took him to the appointment, I held him and talked to him the entire time. I kind of expected to feel some guilt afterward, or wonder if it was the right decision or the right time, but I don't. Of course I miss him terribly and I can't stop crying, but I also feel happy for him. I knew he was treated terribly by his previous owner, and I never wanted him to suffer while in my care. So I feel like, given the situation, it was perfect. Is this normal?