Proof: Multiply Reorder 2

Let's prove the following theorem:

Proof:

Proof Table

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

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