Proof: Division is Commutative

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	b / c = b ⋅ (1 / c)	b / c = b ⋅ (1 / c) (Division is Multiplication by Inverse)
2	(a ⋅ b) / c = (a ⋅ b) ⋅ (1 / c)	(a ⋅ b) / c = (a ⋅ b) ⋅ (1 / c) (Division is Multiplication by Inverse)
3	(a ⋅ b) ⋅ (1 / c) = a ⋅ (b ⋅ (1 / c))	(a ⋅ b) ⋅ (1 / c) = a ⋅ (b ⋅ (1 / c)) (Associative Property of Multiplication)
4	a ⋅ (b ⋅ (1 / c)) = a ⋅ (b / c)	if b / c = b ⋅ (1 / c), then a ⋅ (b ⋅ (1 / c)) = a ⋅ (b / c) (Multiplicative Property of Equality Variation 2)
5	(a ⋅ b) ⋅ (1 / c) = a ⋅ (b / c)	if (a ⋅ b) ⋅ (1 / c) = a ⋅ (b ⋅ (1 / c)) and a ⋅ (b ⋅ (1 / c)) = a ⋅ (b / c), then (a ⋅ b) ⋅ (1 / c) = a ⋅ (b / c) (Transitive Property of Equality)
6	a ⋅ (b / c) = (a ⋅ b) / c	if (a ⋅ b) / c = (a ⋅ b) ⋅ (1 / c) and (a ⋅ b) ⋅ (1 / c) = a ⋅ (b / c), then a ⋅ (b / c) = (a ⋅ b) / c (Transitive Property of Equality Variation 3)

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