Problem: Prove the following,

if b,d 0

I'm sorry to say I analyze this utterly elementary proof to the point of being unable to move.

Proof from book:

by (iii) =

the book then cites the following proof as justification for the latter equivalence:

(iii) = if a,b \not= 0

proof of (iii) from book,

I get that

I also understand that

There is a continuity gap in my comprehension, educate me please.