I am doing the problem 1.2 in book Mathematics for computer science by Lehman.
The problem is as follows:

Prove that if 1 = -1 then 2 = 1.

Proof:
Let A be the proposition 1 > 0.
This proposition obviously holds.
Now, let B be the proposition that 1 <= 0. 
Since 1 = -1 and -1 <= 0, B holds as well.
Now, B is the negation of A. So B = not (A).
Finally, let C be the proposition that 2 = 1.
From not (A) we can deduce not (A) or C, or equivalently A => C.
And since A holds, C holds as well.

Does this proof as it stands solve the problem?