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

Question:

Provide reasons (mostly vector space properties) as justification for each of the seven steps of the following proof.
Theorem
For any vectors u, v, w ∈ Cm, if u + v = u + w, then v = w.
Proof: Let u, v, w ∈ Cm, and suppose u + v = u + w.
v = 0 + v
= (-u + u) + v
= -u + (u + v)
= -u + (u + w)
= (-u + u) + w
= 0 + w
= w