I'm trying to prove this a different way, but I thought I have it but noticed a problem I think that kills it and I need to make sure it's correct that I can't do this. This is what I have...

1) 0=0

2) a0=a0

3) a0=a(1-1)

4) a0=a-a

5) a0=0

The problem is going from step 3 to step 4. Isn't this invoking the other theorem of (-a)b=-ab which requires the proof of a0=0?