Proof: Multiply Both Sides 2

Let's prove the following theorem:

if the following are true:
  • a = b / c
  • not (c = 0)

then c ⋅ a = b

Proof:

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Given
1 a = b / c
2 not (c = 0)
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 if not (c = 0), then (b / c) ⋅ c = b
3 a ⋅ c = b if (b / c) ⋅ c = b and a ⋅ c = (b / c) ⋅ c, then a ⋅ c = b
4 a ⋅ c = c ⋅ a a ⋅ c = c ⋅ a
5 c ⋅ a = b if a ⋅ c = b and a ⋅ c = c ⋅ a, then c ⋅ a = b

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