Provide reasons (mostly vector space properties) as justification for each of the six steps of the following

Question:

Provide reasons (mostly vector space properties) as justification for each of the six steps of the following proof.
Theorem
For any scalar c, c0 = 0.
Proof: Let c be an arbitrary scalar.
0 = c0 + (-c0)
= c(0 + 0) + (-c0)
= (c0 + c0) + (-c0)
= c0 + (c0 + (-c0))
= c0 + 0
= c0