Proof: Subtract Commutative 2

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	(a ⋅ (-1)) + a = 0	(a ⋅ (-1)) + a = 0 (subtract_commutative)
2	a ⋅ (-1) = (-1) ⋅ a	a ⋅ (-1) = (-1) ⋅ a (Commutative Property of Multiplication)
3	((-1) ⋅ a) + a = 0	if (a ⋅ (-1)) + a = 0 and a ⋅ (-1) = (-1) ⋅ a, then ((-1) ⋅ a) + a = 0 (Substitution 8)

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