Proof: Additive Inverse 2

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	a + (a ⋅ (-1)) = 0	a + (a ⋅ (-1)) = 0 (Additive Inverse Property)
2	a ⋅ (-1) = (-1) ⋅ a	a ⋅ (-1) = (-1) ⋅ a (Commutative Property of Multiplication)
3	a + (a ⋅ (-1)) = a + ((-1) ⋅ a)	if a ⋅ (-1) = (-1) ⋅ a, then a + (a ⋅ (-1)) = a + ((-1) ⋅ a) (Substitution)
4	a + ((-1) ⋅ a) = 0	if a + (a ⋅ (-1)) = a + ((-1) ⋅ a) and a + (a ⋅ (-1)) = 0, then a + ((-1) ⋅ a) = 0 (Transitive Property of Equality Variation 2)

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