Proof: Multiply Both Sides 2

Let's prove the following theorem:

if a = b / c, then c ⋅ a = b

Proof:

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Given
1 a = b / c
Proof Table
# Claim Reason
1 a ⋅ c = (b / c) ⋅ c if a = b / c, then a ⋅ c = (b / c) ⋅ c
2 (b / c) ⋅ c = b (b / c) ⋅ c = b
3 a ⋅ c = b if a ⋅ c = (b / c) ⋅ c and (b / c) ⋅ c = b, then a ⋅ c = b
4 a ⋅ c = c ⋅ a a ⋅ c = c ⋅ a
5 c ⋅ a = b if a ⋅ c = c ⋅ a and a ⋅ c = b, then c ⋅ a = b

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