Proof: Reorder Terms 9

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	(b / c) ⋅ c = (b ⋅ (1 / c)) ⋅ c	if b / c = b ⋅ (1 / c), then (b / c) ⋅ c = (b ⋅ (1 / c)) ⋅ c (Multiplicative Property of Equality)
3	(b ⋅ (1 / c)) ⋅ c = (b ⋅ c) ⋅ (1 / c)	(b ⋅ (1 / c)) ⋅ c = (b ⋅ c) ⋅ (1 / c) (Swap Terms 2 and 3)
4	(b ⋅ c) ⋅ (1 / c) = (b ⋅ c) / c	(b ⋅ c) ⋅ (1 / c) = (b ⋅ c) / c (division_theorem)
5	(b / c) ⋅ c = (b ⋅ c) / c	if (b ⋅ c) ⋅ (1 / c) = (b ⋅ c) / c and (b ⋅ (1 / c)) ⋅ c = (b ⋅ c) ⋅ (1 / c) and (b / c) ⋅ c = (b ⋅ (1 / c)) ⋅ c, then (b / c) ⋅ c = (b ⋅ c) / c (Transitive Property Application 1)

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