Proof: Subtract Commutative

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 + (a ⋅ (-1)) = (a ⋅ (-1)) + a	a + (a ⋅ (-1)) = (a ⋅ (-1)) + a (Commutative Property of Addition)
3	(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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