The OP asks for proof. Proof is a tricky thing. What we know and what we can prove are often different. Our world is not just facts, numbers, statistics, and studies. Sometimes our personal experience teaches things we cannot quantify...
So here is my story of vaping. Vaping has been a very important thing in my life. I have ADHD, and I refuse to take Ritalin or any of that stuff. I find that will caffeine and nicotine I can manage my runaway energy and lack of focus quite well. Many people who have known me for years would never guess I am ADHD. So I had to keep using nicotine. Smoking was the only way I could have it that satisfied my need for nicotine "on demand" when I really needed to focus. The gums were ineffective and made me hiccup constantly and want to puke, as did the lozenges. The patches were not effective due to their inability to deliver a hit of nicotine on demand when I really needed focus.
I started vaping in late May 2012. I weighed 268 pounds and was in terrible shape, couldn't breathe well, and had trouble sleeping. I had been smoking for 26 years at the time. I started with a humble eGo starter kit. Quickly I got into twists, then clearos, then mods, etc. Along the way, I started feeling better each day.
Today, I weigh 222 pounds (not bad, at 6'2"), can run and play basketball with my teenage sons, and sleep like I always wished I could almost every night. When we play shirts VS. skins basketball, I don't cringe when I have take my shirt off, nor does anyone else. When I started vaping, my breathing improved right away. I was able to start being much more active. This led me to changes in my diet (no sugar, no starches, no processed food) that also improved my health. So, maybe vaping didn't save my life, but it has made it 10X better. Sure, I made good decisions on top of vaping, but I don't think I would have started down this path without that catalyst.
I am passionate about this issue. I want other smokers to see and enjoy the benefits of it. For this reason, I defend my (and others) opportunity to have access to vaping, and suitable places to vape in, with extreme prejudice. I want everyone to feel this good.
Can I prove vaping saved my life? No way. I don't need to, anyway. I know it has made it so much better that I don't worry about proof. I just know it, balls to bones.