Proof: Reordering Terms Theorem

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	(a ⋅ b) ⋅ c = (a ⋅ c) ⋅ b	(a ⋅ b) ⋅ c = (a ⋅ c) ⋅ b (Swap 2 and 3 Theorem)
2	a ⋅ c = c ⋅ a	a ⋅ c = c ⋅ a (Commutative Property of Multiplication)
3	(a ⋅ c) ⋅ b = (c ⋅ a) ⋅ b	if a ⋅ c = c ⋅ a, then (a ⋅ c) ⋅ b = (c ⋅ a) ⋅ b (Multiplicative Property of Equality)
4	(a ⋅ b) ⋅ c = (c ⋅ a) ⋅ b	if (a ⋅ b) ⋅ c = (a ⋅ c) ⋅ b and (a ⋅ c) ⋅ b = (c ⋅ a) ⋅ b, then (a ⋅ b) ⋅ c = (c ⋅ a) ⋅ b (Transitive Property of Equality)

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