Proof: Subtract Commutative 2

Let's prove the following theorem:

((-1) ⋅ a) + a = 0

Proof:

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Proof Table
# Claim Reason
1 (a ⋅ (-1)) + a = 0 (a ⋅ (-1)) + a = 0
2 a ⋅ (-1) = (-1) ⋅ a a ⋅ (-1) = (-1) ⋅ a
3 ((-1) ⋅ a) + a = 0 if (a ⋅ (-1)) + a = 0 and a ⋅ (-1) = (-1) ⋅ a, then ((-1) ⋅ a) + a = 0

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